[ADMY75] A.Ash, D.Mumford, M.Rapoport, and Y.Tai, Smooth Compactification of Locally Symmetric Varieties, Math. Science Press, Brookline, 1975.
On Affine Structures Which Come from Berkovich Geometry for fqav 93
[AET19]
[BBI01]
[Ber90]
[Ber99]
[Ber10]
[BFJ16]
[BGR84]
[BJ17]
[BL04]
[BM19]
[Del72]
[dFKX17]
[FC90]
[Gel41]
[GH84]
[GO22]
[Got20]
[Got22]
[Gro61]
V. Alexeev, P. Engel, and A. Thompson, Stable pair compactification of moduli
of K3 surfaces of degree 2, arXiv:1903.09742, 2019.
D. Burago, Y. Burago, and S. Ivanov, A course in metric geometry, Graduate
Studies in Mathematics, vol. 33, American Mathematical Society, 2001.
V. Berkovich, Spectral Theory and Analytic Geometry Over Non-Archimedean
Fields, American Mathematical Society, 1990.
, Smooth p-adic analytic spaces are locally contractible, Inventiones
mathematicae 137 (1999), 1–84.
, A non-Archimedean interpretation of the weight zero subspaces of
limit mixed Hodge structures in Algebra, Arithmetic and Geometry. Volume I:
In Honor of Y.I. Manin, Progress in Mathematics 269 (2010), 49–67.
S. Boucksom, C. Favre, and M. Jonsson, Singular semipositive metrics in
non-Archimedean geometry, Journal of Algebraic Geometry 25 (2016), no. 1,
77–139.
S. Bosch, U. Güntzer, and R. Remmert, Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Grundlehren der mathematischen
Wissenschaften, Springer-Verlag, 1984.
S. Boucksom and M. Jonsson, Tropical and non-Archimedean limits of degenerating families of volume forms, Journal de l’École polytechnique - Mathématiques 4 (2017), 87–139.
C. Birkenhake and H. Lange, Complex Abelian varieties, Die Grundlehren der
mathematischen Wissenschaften, vol. 302, Springer-Verlag, 2004.
M. Brown and E. Mazzon, The Essential Skeleton of a product of degenerations, Compositio Mathematica 155 (2019), no. 7, 1259–1300.
P. Deligne, Résumé des premiers exposés de A. Grothendieck. In: Groupes de
Monodromie en Géométrie Algébrique (SGA 7), Lecture Notes in Mathematics, vol. 288, Springer, Berlin, Heidelberg, 1972.
T. de Fernex, J. Kollár, and C. Xu, The dual complex of singularities -in honour
of Professor Yujiro Kawamata’s sixtieth birthday, Advanced Studies in Pure
Mathematics 74 (2017), 103–129.
G. Faltings and C. L. Chai, Degeneration of abelian varieties, Ergebnisse der
Mathematik und ihrer Grenzgebiete (3), vol. 22, Springer-Verlag, Berlin, 1990.
I. Gelfand, Normierte ringe, Matematicheskii Sbornik Novaya Seriya 9(51)
(1941), 3–24.
W. Goldman and M. W. Hirsch, The radiance obstruction and parallel forms
on affine manifolds, Transactions of the American Mathematical Society 286
(1984), no. 2, 629–649.
K. Goto and Y. Odaka, Special Lagrangian fibrations, Berkovich retraction,
and crystallographic groups, arXiv:2206.14474, 2022 (submitted).
K. Goto, On the Berkovich double residue fields and birational models,
arXiv:2007.03610, 2020 (submitted).
, On The Two Types Of Affine Structures For Degenerating Kummer
Surfaces Non-Archimedean VS Gromov-Hausdorff Limits, arXiv:2203.14543,
2022 (submitted).
A. Grothendieck, éléments de géométrie algébrique : III. étude cohomologique des faisceaux cohérents, Première partie, Publications Mathématiques de l’IHÉS 11 (1961), 5–167 (fr).
94 Keita Goto
M. Gromov, Structures métriques pour les variétés riemanniennes, Textes
mathématiques. Recherche, CEDIC/Fernand Nathan, 1981.
[Gro13]
M. Gross, Mirror Symmetry and the Strominger-Yau-Zaslow conjecture, Current developments in mathematics 2012 (2013), 133–191.
[GS06]
M. Gross and B. Siebert, Mirror Symmetry via Logarithmic Degeneration
Data I, Journal of Differential Geometry 72 (2006), no. 2, 169–338.
[Har77]
R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol. 52,
Springer-Verlag, 1977.
[Hit97]
N. J. Hitchin, The moduli space of special lagrangian submanifolds, Annali
della Scuola Normale Superiore di Pisa - Classe di Scienze Ser. 4, 25 (1997),
no. 3-4, 503–515.
[HL82]
R. Harvey and H. B. Lawson, Calibrated geometries, Acta Mathematica 148
(1982), 47–157.
[HN17]
L. H. Halle and J. Nicaise, Motivic zeta functions of degenerating Calabi–Yau
varieties, Mathematische Annalen 370 (2017), 1277–1320.
[JM13]
M. Jonsson and M. Mustaţă, Valuations and asymptotic invariants for sequences of ideals, Université de Grenoble. Annales de l’Institut Fourier 62
(2013), no. 6, 2145–2209.
[Jon16]
M. Jonsson, Degenerations of amoebae and Berkovich spaces, Mathematische
Annalen 364 (2016), no. 1-2, 293–311.
[KKMS73] G. Kempf, F. Knudsen, D. Mumford, and B. Saint-Donat, Toroidal Embeddings, Lecture notes in mathematics, Springer-Verlag, 1973.
[Kob05]
S. Kobayashi, Complex geometry, Iwanami Shoten, 2005 (jp).
[KS06]
M. Kontsevich and Y. Soibelman, Affine Structures and Non-Archimedean Analytic Spaces, The Unity of Mathematics: In Honor of the Ninetieth Birthday
of I.M. Gelfand (2006), 321–385.
[Kün98]
K. Künnemann, Projective regular models for abelian varieties, semistable reduction, and the height pairing, Duke Mathematical Journal 95 (1998), no. 1,
161 – 212.
[Li20]
Y. Li, Metric SYZ conjecture and non-archimedean geometry,
arXiv:2007.01384, 2020.
[Liu11]
Y. Liu, A non-archimedean analogue of Calabi-Yau theorem for totally degenerate abelian varieties , Journal of Differential Geometry 89 (2011), 87–110.
[LP20]
T. Lemanissier and J. Poineau, Espaces de berkovich sur Z : catégorie, topologie, cohomologie, arXiv:2010.08858, 2020.
[Mat16]
Y. Matsumoto, Degeneration of K3 surfaces with non-symplectic automorphisms, to appear in Rendiconti del Seminario Matematico della Universitá di
Padova (2016).
[MN12]
M. Mustaţă and J. Nicaise, Weight functions on non-Archimedean analytic
spaces and the Kontsevich-Soibelman skeleton, Algebraic Geometry 2 (2012).
[MN22]
K. Mitsui and I. Nakamura, Relative compactifications of semiabelian Néron
models, arXiv:2201.08113, 2022.
[MS84]
J. Morgan and P. Shalen, Valuations, trees, and degenerations of hyperbolic
structures, I, Annals of Mathematics. (2) 120 (1984), no. 3, 401–476.
[Mum70] D. Mumford, Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics, vol. 5, Oxford University Press, 1970.
, An analytic construction of degenerating abelian varieties over com[Mum72]
plete rings, Compositio Mathematica 24 (1972), no. 3, 239–272.
[Gro81]
On Affine Structures Which Come from Berkovich Geometry for fqav 95
[NX16]
[NXY19]
[Oda19]
[OO21]
[Ove21]
[Poi10]
[Poi13]
[PS22]
[Ray74]
[RS82]
[SYZ96]
[Tem08]
[Tsu20]
J. Nicaise and C. Xu, The essential skeleton of a degeneration of algebraic
varieties, American Journal of Mathematics 138 (2016), no. 6, 1645–1667.
J. Nicaise, C. Xu, and T. Y. Yu, The non-archimedean SYZ fibration, Compositio Mathematica 155 (2019), no. 5, 953–972.
Y. Odaka, Tropical Geometric Compactification of Moduli, II: Ag Case and
Holomorphic Limits, International Mathematics Research Notices (2019),
no. 21, 6614–6660.
Y. Odaka and Y. Oshima, Collapsing K3 Surfaces, Tropical Geometry and
Moduli Compactifications of Satake, Morgan-Shalen Type, MSJ Memoir,
vol. 40, MATHEMATICAL SOCIETY OF JAPAN, 2021.
O. Overkamp, Degeneration of Kummer surfaces, Mathematical Proceedings
of the Cambridge Philosophical Society 171 (2021), no. 1, 65–97.
J. Poineau, La droite de Berkovich sur Z, Astérisque, no. 334, Société mathématique de France, 2010 (fr).
, Espaces de Berkovich sur Z : étude locale, Inventiones mathematicae
194 (2013), 535–590 (fr).
L. Pille-Schneider, Hybrid toric varieties and the non-archimedean syz fibration on calabi-yau hypersurfaces, arXiv:2210.05578, 2022.
M. Raynaud, Géométrie analytique rigide d’après Tate, Kiehl..., Mémoires de
la Société Mathématique de France (1974), no. 39-40, 319–327.
C.P. Rourke and B.J. Sanderson, Introduction to piecewise-linear topology,
Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, 1982.
A. Strominger, S.-T. Yau, and E. Zaslow, Mirror symmetry is T duality, Nuclear
Physics 479 (1996), 243–259.
M. Temkin, Desingularization of quasi-excellent schemes in characteristic
zero, Advances in Mathematics 219 (2008), no. 2, 488 – 522.
Y. Tsutsui, On the radiance obstruction of some tropical surfaces, Proceeding
to The 16th Mathematics Conference for Young Researchers, 2020 (jp).
Department of Mathematics, Kyoto university, Oiwake-cho, Kitashirakawa,
Sakyo-ku, Kyoto city,Kyoto 606-8285. JAPAN
Email address: k.goto@math.kyoto-u.ac.jp
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