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referencies.bib

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+@article{canonical,
+  title={A canonical bundle formula},
+  author={Fujino, Osamu and Mori, Shigefumi},
+  journal={Journal of Differential Geometry},
+  volume={56},
+  number={1},
+  pages={167--188},
+  year={2000},
+  publisher={Lehigh University},
+  url={\url{https://www.math.kyoto-u.ac.jp/~fujino/Canonical.pdf}}
+}
+@inproceedings{KLSV,
+  Author = {Koll{\'a}r, J{\'a}nos and Laza, Radu and Sacc{\`a}, Giulia and Voisin, Claire},
+ Title = {Remarks on degenerations of hyper-{K{\"a}hler} manifolds},
+ journal = {Annales de l'Institut Fourier},
+ ISSN = {0373-0956},
+ Volume = {68},
+ Number = {7},
+ Pages = {2837--2882},
+ Year = {2018}
+}
+
+@article{fujino,
+  title={Semi-stable minimal model program for varieties with trivial canonical divisor},
+  author={Fujino, Osamu},
+  pages={25-30},
+  volume={87},
+  number={3},
+  journal={Proc. Japan Acad. Ser. A Math. Sci.},
+  year={2011}
+}
+
+@book{KM, place={Cambridge}, series={Cambridge Tracts in Mathematics}, title={Birational Geometry of Algebraic Varieties}, publisher={Cambridge University Press}, author={Kollár, János and Mori, Shigefumi}, year={1998}, volume={134}, collection={Cambridge Tracts in Mathematics}}
+
+@book{kollar,
+  Author = {Koll{\'a}r, J{\'a}nos},
+ Title = {Singularities of the minimal model program.},
+ series = {Cambridge Tracts in Mathematics},
+ ISSN = {0950-6284},
+ Volume = {200},
+ ISBN = {978-1-107-03534-8; 978-1-139-54789-5},
+ Year = {2013},
+ Publisher = {Cambridge University Press}
+}
+@article{PP,
+  title={Degeneration of surfaces with trivial canonical bundle},
+  author={Persson, Ulf and Pinkham, Henry},
+  journal={Annals of Mathematics},
+  pages={45--66},
+  volume={113},
+  year={1981},
+  publisher={JSTOR}
+}
+@article{kulikov,
+  title={Degenerations of {K}3 surfaces and {E}nriques surfaces},
+  author={Kulikov, Viktor},
+  journal={Mathematics of the USSR-Izvestiya},
+  volume={11},
+  number={5},
+  pages={957},
+  year={1977},
+  publisher={IOP Publishing}
+}
+@article{kawamata,
+  title={Flops connect minimal models},
+  author={Kawamata, Yujiro},
+  journal={Publications of the research institute for mathematical sciences},
+  volume={44},
+  number={2},
+  pages={419--423},
+  year={2008},
+  url={arXiv:0704.1013}
+}
+@incollection{KMM,
+  title={Introduction to the minimal model problem},
+  author={Kawamata, Yujiro and Matsuda, Katsumi and Matsuki, Kenji},
+  booktitle={Algebraic geometry, Sendai, 1985},
+  volume={10},
+  pages={283--361},
+  year={1987},
+  publisher={Mathematical Society of Japan}
+}
+@article{deFernex,
+  title={The dual complex of singularities},
+  author={de Fernex, Tommaso and Koll{\'a}r, J{\'a}nos and Xu, Chenyang},
+  journal={Higher dimensional algebraic geometry—in honour of Professor Yujiro Kawamata’s sixtieth birthday},
+  volume={74},
+  pages={103--129},
+  year={2017}
+}
+
+@article{kollarxu,
+   title={The dual complex of {C}alabi–{Y}au pairs},
+   volume={205},
+   ISSN={1432-1297},
+   url={http://dx.doi.org/10.1007/s00222-015-0640-6},
+   DOI={10.1007/s00222-015-0640-6},
+   number={3},
+   journal={Inventiones mathematicae},
+   publisher={Springer Science and Business Media LLC},
+   author={Kollár, János and Xu, Chenyang},
+   year={2015},
+   month=dec, pages={527–557} }
+@article{reid,
+  title={Young person’s guide to canonical singularities},
+  author={Reid, Miles},
+  journal={Algebraic geometry, Bowdoin},
+  volume={46},
+  pages={345--414},
+  year={1985}
+}
+@article{namikawa,
+  title={Global smoothing of {C}alabi-{Y}au threefolds},
+  author={Namikawa, Yoshinori and Steenbrink, Joseph},
+  journal={Inventiones mathematicae},
+  year={1995},
+  volume={122},
+  pages={403-419},
+  url={https://api.semanticscholar.org/CorpusID:122698510}
+}
+@article{kawamata85,
+  title={Minimal models and the {K}odaira dimension of algebraic fiber spaces.},
+  author={Yūjirō Kawamata},
+  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
+  year={1985},
+  volume={1985},
+  pages={1 - 46},
+  url={https://api.semanticscholar.org/CorpusID:116957463}
+}
+@misc{grassi,
+      title={On topological invariants of algebraic threefolds with ($\mathbb Q$-factorial) singularities}, 
+      author={Antonella Grassi and Timo Weigand},
+      year={2018},
+      eprint={1804.02424},
+      archivePrefix={arXiv},
+      primaryClass={math.AG}
+}
+@misc{schwald,
+      title={Low degree {H}odge theory for klt varieties}, 
+      author={Martin Schwald},
+      year={2016},
+      eprint={1612.01919},
+      archivePrefix={arXiv},
+      primaryClass={math.AG}
+}
+@article{fujinodlt,
+  title={{W}hat is log terminal?},
+  journal={Flips for 3-folds and 4-folds},
+  author={{F}ujino, {O}samu},
+  year={2007},
+  pages={49-62},
+  publisher={Oxford University Press},
+  series={Oxford Lecture Ser. Math. Appl.},
+  volume={35}
+}
+
+@inproceedings{vaquie,
+  title={R{\'e}solution simultan{\'e}e d'une famille de singularit{\'e}s rationnelles de surface normale},
+  author={Vaqui{\'e}, Michel},
+  booktitle={Annales de l'institut Fourier},
+  volume={35},
+  number={4},
+  pages={1--37},
+  year={1985}
+}
+
+@inproceedings{laufer,
+  title={Weak simultaneous resolution for deformations of {G}orenstein surface singularities},
+  author={Laufer, Henry B},
+  booktitle={Proc. Sympos. Pure Math.},
+  volume={40},
+  pages={1--29},
+  year={1983}
+}
+@article{artin,
+  title={Algebraic construction of {B}rieskorn's resolutions},
+  author={Artin, Michael},
+  journal={Journal of Algebra},
+  volume={29},
+  number={2},
+  pages={330--348},
+  year={1974},
+  publisher={Elsevier}
+}
+@article{kollarthreefolds,
+  title={Threefolds and deformations of surface singularities},
+  author={Kollár, János and Shepherd-Barron, Nicholas},
+  journal={Inventiones mathematicae},
+  volume={91},
+  pages={299--338},
+  year={1988},
+  publisher={Springer-Verlag}
+}
+@article{factorial,
+ ISSN = {0003486X, 19398980},
+ URL = {http://www.jstor.org/stable/1971417},
+ author = {Kawamata, Yujiro},
+ journal = {Annals of Mathematics},
+ number = {1},
+ pages = {93--163},
+ publisher = {[Annals of Mathematics, Trustees of Princeton University on Behalf of the Annals of Mathematics, Mathematics Department, Princeton University]},
+ title = {Crepant blowing-up of 3-dimensional canonical Singularities and its application to degenerations of surfaces},
+ volume = {127},
+ year = {1988}
+}
+
+@article{friedmanbase,
+  title={Base change, automorphisms, and stable reduction for type {III} {K}3 surfaces},
+  author={Friedman, Robert},
+  journal={The birational geometry of degenerations (Cambridge, Mass., 1981)},
+  volume={29},
+  pages={277--298},
+  year={1983}
+}
+
+
+@book{mumford,
+  Author = {Kempf, G. and Knudsen, F. and Mumford, D. and Saint-Donat, Bernard},
+ Title = {Toroidal embeddings. {I}},
+ FSeries = {Lecture Notes in Mathematics},
+ Series = {Lect. Notes Math.},
+ ISSN = {0075-8434},
+ Volume = {339},
+ Year = {1973},
+ Publisher = {Springer}
+}
+@article{horing,
+  title={Minimal models for {K}{\"a}hler threefolds},
+  author={H{\"o}ring, Andreas and Peternell, Thomas},
+  journal={Inventiones mathematicae},
+  volume={203},
+  number={1},
+  pages={217--264},
+  year={2016},
+  publisher={Springer}
+}
+
+@article{counterexample,
+  title={Degeneration of {K}3 surfaces},
+  author={Nishiguchi, Kenji},
+  journal={Journal of Mathematics of Kyoto University},
+  volume={28},
+  number={2},
+  pages={267--300},
+  year={1988},
+  publisher={Duke University Press}
+}
+
+@article{iskovskikh,
+  title={Minimal models of rational surfaces over arbitrary fields},
+  author={Iskovskikh, Vasilii Alekseevich},
+  journal={Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya},
+  volume={43},
+  number={1},
+  pages={19--43},
+  year={1979},
+  publisher={Russian Academy of Sciences, Steklov Mathematical Institute of Russian}
+}
+
+
+@article{kollarreal,
+  Author = {Koll{\'a}r, J{\'a}nos},
+ Title = {Real algebraic threefolds. {II}: {Minimal} model program},
+ FJournal = {Journal of the American Mathematical Society},
+ Journal = {J. Am. Math. Soc.},
+ ISSN = {0894-0347},
+ Volume = {12},
+ Number = {1},
+ Pages = {33--83},
+ Year = {1999}
+}
+
+@article{hironaka,
+  title={Resolution of singularities of an algebraic variety over a field of characteristic zero: {II}},
+  author={Hironaka, Heisuke},
+  journal={Annals of Mathematics},
+  volume={79},
+  number={2},
+  pages={205--326},
+  year={1964},
+  publisher={JSTOR}
+}
+
+@inproceedings{duval,
+  title={On isolated singularities of surfaces which do not affect the conditions of adjunction {I-III}},
+  author={du {V}al, Patrick},
+  booktitle={Proc. Camb. Phil. Soc.,},
+  volume={30},
+  pages={453-465,483-491},
+  year={1934}
+}
+
+@inproceedings{brieskorn,
+  title={Singular elements of semi-simple algebraic groups},
+  author={Brieskorn, Egbert},
+  booktitle={Proc. Int. Cong. Math., Nice},
+  publisher={Gauthier-Villars},
+  year={1971}
+}
+
+@book{kollarMMP,
+  title={Flips and abundance for algebraic threefolds: A summer seminar at the University of Utah (Salt Lake City, 1991)},
+  author={Kollár, János and Abramovich, Dan},
+  year={1992},
+  publisher={Soci{\'e}t{\'e} math{\'e}matique de France}
+}
+
+@book{hartshorne,
+  title={Algebraic geometry},
+  author={Hartshorne, Robin},
+  volume={52},
+  year={2013},
+  publisher={Springer Science \& Business Media}
+}
+
+@article{moriflip,
+  title={Flip theorem and the existence of minimal models for 3-folds},
+  author={Mori, Shigefumi},
+  journal={Journal of the American Mathematical Society},
+  volume={1},
+  number={1},
+  pages={117--253},
+  year={1988},
+  publisher={JSTOR}
+}
+
+@article{positive,
+  title={Semistable minimal models of threefolds in positive or mixed characteristic},
+  author={Kawamata, Yujiro},
+  journal={Journal of Algebraic Geometry},
+  volume={3},
+  number={3},
+  pages={463},
+  year={1994}
+}
+
+@article{realkollarI,
+   Author = {Koll{\'a}r, J{\'a}nos},
+ Title = {Real algebraic threefolds. {I}: {Terminal} singularities},
+ Journal = {Collectanea Mathematica},
+ ISSN = {0010-0757},
+ Volume = {49},
+ Number = {2-3},
+ Pages = {335--360},
+ Year = {1998}
+}
+
+@article{steenbrink,
+  title={Cohomologically insignificant degenerations},
+  author={Steenbrink, Joseph HM},
+  journal={Compositio Mathematica},
+  volume={42},
+  number={3},
+  pages={315--320},
+  year={1980}
+}
+
+@article{steenbrinkLMHS,
+  title={Limits of {H}odge structures},
+  author={Steenbrink, Joseph},
+  journal={Inventiones mathematicae},
+  volume={31},
+  number={3},
+  pages={229--257},
+  year={1976},
+  publisher={Springer-Verlag Berlin/Heidelberg}
+}
+
+@book{deligne,
+  title={Th{\'e}orie de {H}odge},
+  author={Deligne, Pierre},
+  year={1970},
+  publisher={Institut des Hautes Etudes Scientifiques}
+}
+
+@article{schmid,
+  title={Variation of {H}odge structure: the singularities of the period mapping},
+  author={Schmid, Wilfried},
+  journal={Inventiones mathematicae},
+  volume={22},
+  number={3},
+  pages={211--319},
+  year={1973},
+  publisher={Springer-Verlag Berlin/Heidelberg}
+}
+
+@article{nicaise,
+  title={The non-archimedean {SYZ}fibration},
+  author={Nicaise, Johannes and Xu, Chenyang and Yu, Tony Yue},
+  journal={Compositio Mathematica},
+  volume={155},
+  number={5},
+  pages={953--972},
+  year={2019},
+  publisher={London Mathematical Society}
+}
+
+@book{friedman,
+  title={The Birational Geometry of Degenerations},
+  author={Friedman, Robert and Morrison, David R.},
+  series={Progress in mathematics},
+  volume={29},
+  year={1983},
+  publisher={Birkh{\"a}user}
+}
+@book{badescu,
+author="B{\u{a}}descu, Lucian",
+title="Algebraic {S}urfaces",
+bookTitle="Algebraic Surfaces",
+year="2001",
+publisher="Springer New York",
+address="New York, NY",
+isbn="978-1-4757-3512-3",
+}
+
+@book{persson,
+   Author = {Persson, Ulf},
+ Title = {On degenerations of algebraic surfaces},
+ series = {Memoirs of the American Mathematical Society},
+ ISSN = {0065-9266},
+ Volume = {189},
+ ISBN = {978-0-8218-2189-3; 978-1-4704-0103-0},
+ Year = {1977},
+ Publisher = {American Mathematical Society},
+}
+
+@article{albanese,
+  title={On {A}lbanese torsors and the elementary obstruction},
+  author={Wittenberg, Olivier},
+  journal={Mathematische Annalen},
+  volume={340},
+  pages={805--838},
+  year={2008},
+  publisher={Springer}
+}
+
+
+@book{ADEtoric,
+  title={Toric varieties},
+  author={Cox, David A and Little, John B and Schenck, Henry K},
+  volume={124},
+  year={2024},
+  publisher={American Mathematical Society}
+}
+
+@book{beauville,
+  title={Complex algebraic surfaces},
+  author={Beauville, Arnaud},
+  year={1996},
+  publisher={Cambridge University Press}
+}
+@book{fulton,
+ Author = {Fulton, William},
+ Title = {Introduction to toric varieties},
+ series = {Annals of Mathematics Studies},
+ Series = {Ann. Math. Stud.},
+ Volume = {131},
+ ISBN = {0-691-00049-2},
+ Year = {1993},
+ Publisher = {Princeton, NJ: Princeton University Press}
+}
+
+@misc{milne,
+author={Milne, James S.},
+title={Abelian Varieties (v2.00)},
+year={2008},
+note={Available at www.jmilne.org/math/},
+pages={166+vi}
+}
+
+@article{boucksom,
+Author = {Boucksom, S{\'e}bastien and Favre, Charles and Jonsson, Mattias},
+ Title = {Singular semipositive metrics in non-{Archimedean} geometry},
+ FJournal = {Journal of Algebraic Geometry},
+ Journal = {J. Algebr. Geom.},
+ ISSN = {1056-3911},
+ Volume = {25},
+ Number = {1},
+ Pages = {77--139},
+ Year = {2016}
+}
+
+@inproceedings{nicaiseberk,
+  title={Berkovich skeleta and birational geometry},
+  author={Nicaise, Johannes},
+  booktitle={Nonarchimedean and tropical geometry},
+  pages={173--194},
+  year={2016},
+  organization={Springer}
+}
+
+@article{shokurov,
+Author = {Iskovskikh, Vasily A. and Shokurov, Vyacheslav V.},
+ Title = {Birational models and flips.},
+ Journal = {Russian Mathematical Surveys},
+ ISSN = {0036-0279},
+ Volume = {60},
+ Number = {1},
+ Pages = {27--94},
+ Year = {2005}
+}
+
+@Article{shokurovsing,
+ Author = {Shokurov, Vyacheslav V.},
+ Title = {Semistable 3-fold flips},
+ Journal = {Russian Academy of Sciences. Izvestiya. Mathematics},
+ ISSN = {1064-5632},
+ Volume = {42},
+ Number = {2},
+ Pages = {371--425},
+ Year = {1993}
+ }
+ 
+ @Article{bchm,
+ Author = {Birkar, Caucher and Cascini, Paolo and Hacon, Christopher D. and McKernan, James},
+ Title = {Existence of minimal models for varieties of log general type},
+ Journal = {Journal of the American Mathematical Society},
+ ISSN = {0894-0347},
+ Volume = {23},
+ Number = {2},
+ Pages = {405--468},
+ Year = {2010}
+ }
+ 
+ @article{zhang,
+ author = {Zhang, Yuguang},
+ title = {Collapsing of {Calabi}-{Yau} manifolds and special {Lagrangian} submanifolds},
+ fjournal = {Zeszyty Naukowe Uniwersytetu Jagiello{\'n}skiego. Universitatis Iagellonicae Acta Mathematica},
+ journal = {Zesz. Nauk. Uniw. Jagiell., Univ. Iagell. Acta Math.},
+ issn = {0083-4386},
+ volume = {54},
+ pages = {53--78},
+ year = {2017}
+ }
+ 
+ @incollection{kontsevich,
+ author = {Kontsevich, Maxim and Soibelman, Yan},
+ title = {Homological mirror symmetry and torus fibrations.},
+ booktitle = {Symplectic geometry and mirror symmetry. Proceedings of the 4th KIAS annual international conference, Seoul, South Korea, August 14--18, 2000},
+ isbn = {981-02-4714-1},
+ pages = {203--263},
+ year = {2001},
+ publisher = {Singapore: World Scientific},
+ language = {English}
+ }
+ 
+ @article{metricli,
+ author = {Li, Yang},
+ title = {Metric {SYZ} conjecture and non-{Archimedean} geometry},
+ journal = {Duke Mathematical Journal},
+ issn = {0012-7094},
+ volume = {172},
+ number = {17},
+ pages = {3227--3255},
+ year = {2023}
+ }
+ 
+ @misc{surveyli,
+ author = {Li, Yang},
+ title = {Survey on the metric {SYZ} conjecture and non-archimedean geometry},
+ year = {2022},
+ howpublished = {Preprint, {arXiv}:2204.11363 [math.{AG}] (2022)},
+ doi = {10.1142/S0217751X22300095},
+ url = {https://arxiv.org/abs/2204.11363},
+ arXiv = {arXiv:2204.11363}
+}
+
+@article{solutionboucksom,
+ author = {Boucksom, S{\'e}bastien and Favre, Charles and Jonsson, Mattias},
+ title = {Solution to a non-{Archimedean} {Monge}-{Amp{\`e}re} equation},
+ fjournal = {Journal of the American Mathematical Society},
+ journal = {J. Am. Math. Soc.},
+ issn = {0894-0347},
+ volume = {28},
+ number = {3},
+ pages = {617--667},
+ year = {2015}
+ }
+ 
+ @misc{javierpelka,
+ author = {Fern{\'a}ndez de Bobadilla, Javier and Pe{\l}ka, Tomasz},
+ title = {Fibrations by {Lagrangian} tori for maximal {Calabi}-{Yau} degenerations and beyond},
+ year = {2023},
+ howpublished = {Preprint, {arXiv}:2312.13248 [math.{AG}] (2023)},
+ keywords = {14D06,14J32,32Q25,53C23,53D12},
+ url = {https://arxiv.org/abs/2312.13248},
+ arXiv = {arXiv:2312.13248}
+}
+
+@article{mustatanicaise,
+ author = {Musta{\c{t}}{\u{a}}, Mircea and Nicaise, Johannes},
+ title = {Weight functions on non-{Archimedean} analytic spaces and the {Kontsevich}-{Soibelman} skeleton},
+ fjournal = {Algebraic Geometry},
+ journal = {Algebr. Geom.},
+ issn = {2313-1691},
+ volume = {2},
+ number = {3},
+ pages = {365--404},
+ year = {2015}
+ }
+ @misc{mazzon,
+ author = {Mazzon, Enrica and Pille-Schneider, L{\'e}onard},
+ title = {Toric geometry and integral affine structures in non-archimedean mirror symmetry},
+ year = {2021},
+ howpublished = {Preprint, {arXiv}:2110.04223 [math.{AG}] (2021)},
+ keywords = {05E14,14J32,14J33,32P05},
+ url = {https://arxiv.org/abs/2110.04223},
+ arXiv = {arXiv:2110.04223}
+}
+@article{burgos,
+ author = {Burgos Gil, Jos{\'e} Ignacio and Moriwaki, Atsushi and Philippon, Patrice and Sombra, Mart{\'{\i}}n},
+ title = {Arithmetic positivity on toric varieties},
+ fjournal = {Journal of Algebraic Geometry},
+ journal = {J. Algebr. Geom.},
+ issn = {1056-3911},
+ volume = {25},
+ number = {2},
+ pages = {201--272},
+ year = {2016}
+ }
+
+@article{vilsmeier,
+ author = {Vilsmeier, Christian},
+ title = {A comparison of the real and non-{Archimedean} {Monge}-{Amp{\`e}re} operator},
+ fjournal = {Mathematische Zeitschrift},
+ journal = {Math. Z.},
+ issn = {0025-5874},
+ volume = {297},
+ number = {1-2},
+ pages = {633--668},
+ year = {2021}
+ }