[AV02] D.Abramovich, A.Vistoli, Compactifying the space of stable maps, J. Amer. Math. Soc. 15 (1): 27-75. 2002.
[AN99] V. Alexeev, I. Nakamura, On Mumford’s construction of degenerating abelian va- rieties, Tohoku Math. J. vol. 51, pp.399–420 (1999).
[ABE20] V. Alexeev, A. Brunyate, P. Engel, Compactifications of moduli of elliptic K3 surfaces: stable pairs and toroidal, arXiv:2002.07127v3.
[AET19] V. Alexeev, P. Engel, A. Thompson, Stable pair compactification of moduli of K3 surfaces of degree 2, arXiv:1903.09742.
[Amb05] F. Ambro, The moduli b-divisor of an lc-trivial fibration, Compositio Math. 141 (2005) 385-403
[AP06] C. Arezzo, F. Pacard, Blowing up and desingularizing Ka¨hler orbifolds with con- stant scalar curvature, Acta Math. 196(2) , 179-228 (2006).
[ASD73] M.Artin, H.P.F. Swinnerton-Dyer, The Shafarevich-Tate conjecture for pencils of elliptic curves on K3 surfaces, Invent. Math. 20 (1973), 249-266.
[AMRT] A. Ash, D. Mumford, M. Rapoport, Y.-S. Tai, Smooth compactifications of locally symmetric varieties, Cambridge Mathematical Library, Second edition (2010).
[AB19] K.Ascher, D.Bejleri, Compact moduli spaces of elliptic K3 surfaces, arXiv:1902.10686v3.
[AKO06] D. Auroux, L. Katzarkov, D. Orlov, Mirror symmetry for Del Pezzo surfaces: Vanishing cycles and coherent sheaves, Invent. Math. 166 (2006), no. 3, 537-582.
[BS78] I.N.Bernstein, O.V.Shvartsman, Chevalley’s theorem for complex crystallographic Coxeter groups (Russian), Func. An. Appl. 12 308 (1978).
[BJ17] S. Boucksom, M. Jonsson, Tropical and non-Archimedean limits of degenerating families of volume forms, Journal de l’E´ cole polytechnique - Mathe´matiques, Tome 4 (2017), p. 87-139.
[BL00] J. Bryan, N.C.Leung, The enumerative geometry of K3 surfaces and modular forms, J. Amer. Math. Soc. 13 (2000), no.2, 371-410.
[Brun15] A. Brunyate, A modular compactification of the space of elliptic K3 surfaces, UGA Ph.D thesis (2015).
[CPS] M.Carl, M.Pumperla, B.Siebert, A tropical view on Landau-Ginzburg models, preprint.
[CFG92] J. Cheeger, K. Fukaya, M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992), 327-372.
[CC97] J. Cheeger, T.H. Colding, On the structure of spaces with Ricci curvature bounded below I, J. Differential Geom. 46 (1997), no. 3, 406–480.
[CC21] G. Chen, X.-X. Chen, Gravitational instantons with faster than quadratic curva- ture decay (III), Math. Ann, vol. 380, 687-717 (2021).
[CJL21] T.Collins, A.Jacob, Y-S.Lin, Special Lagrangian submanifolds of log Calabi-Yau manifolds, Duke Math. J. 170 (2021), no. 7, 1291-1375.
[CD07] A. Clingher, C. Doran, Modular invariants for lattice polarized K3 surfaces, Michigan Math. J. 55 (2007), no. 2, 355-393.
[CM05] A. Clingher, J. Morgan, Mathematics underlying the F-theory/heterotic string du- ality in eight dimensions, Comm. in Math. Phys. 254 (3), 513-563 (2005).
[Cox95] D. Cox, The homogenous coordinate ring of a toric variety, J. Algebraic Geom., vol. 4 (1995) 17-50.
[Dav65] H. Davenport, On f 3(t) g2(t), Norske Vid. Slesk. Forh. (Trondheim) 38 (1965), 86-87.
[DHT17] C.F.Doran, A.Harder, A.Thompson, Mirror symmetry, Tyurin degenerations and fibrations on Calabi-Yau manifolds, proceedings of the conference String-Math, 2015, 93-131 (2017).
[Dol96] I.Dolgachev, Mirror symmetry for lattice polarised K3 surfaces, J. Math. Sci. 81 (1996), no.3, 2599-2630.
[Don02] S. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002), no. 2, 289–349.
[Dre04] J-M. Dre´zet, Luna’s slice theorem and applications, Algebraic group actions and quotients, 39-89, Hindawi Publ. Corp., Cairo, (2004).
[EF19] P.Engel, R.Friedman, Smoothings and rational double point adjacencies for cusp singularities, J. Differential Geom. (2019).
[EHX97] T.Eguchi, K.Hori, C-S. Xiong, Gravitational quantum cohomology, Internat. J. Modern Phys. A 12 (1997), no.9, 1743-1782.
[Fjn18] O.Fujino, Semipositivity theorems for moduli problems, Ann. of Math., pp. 639- 665 from Volume 187 (2018),
[Fri84] R. Friedman, A new proof of the global Torelli theorem for K3 surfaces, Ann. of Math. vol. 120, no.2, 237-269 (1984).
[FMW97] R.Friedman, J.Morgan, E.Witten, Vector bundles and F-theory, Commun. Math. Phys. 187. 679-743 (1997).
[Fscl16] L. Foscolo, ALF gravitational instantons and collapsing Ricci-flat metrics on the K3 surface, to appear in J. Differential Geom. (arXiv:1603.06315).
[Freed99] D. Freed, Special Ka¨hler manifolds, Comm. Math. Phys. 203 (1999), no. 1, 31– 52.
[Fri83] R. Friedman, Global smoothings of varieties with normal crossings, Annals of Mathematics, 118 (1983), 75-114
[Fri84] R. Friedman, A new proof of the global Torelli theorem for K3 surfaces, Ann. of Math. (2) 120 (1984), no. 2, 237–269.
[FriMrg94] R. Friedman, J. Morgan, Smooth Four-Manifolds and Complex Surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 27. Springer-Verlag, (1994). [FriMor83] R. Friedman, D. Morrison, The birational geometry of degenerations, Progress in Math. 29, Birkha¨user, (1983).
[FriSca86] R. Friedman, F. Scattone, Type III degenerations of K3 surfaces, Invent. Math. 83 (1986), no. 1, 1–39.
[Fri15] R. Friedman, On the geometry of anticanonical pairs, arXiv:1502.02560.
[Fuk87a] K. Fukaya, Collapsing of Riemannian manifolds and eigenvalues of Laplace op- erator, Invent. Math., 87 (1987), 517-547.
[Fuk87b] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, J. Differential Geom. 25 (1987), 139-156.
[Fuk89] K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, II, J. Math. Soc. Japan 41 (1989), no. 2, 333–356
[GHK15] M. Gross, P.Hacking, S.Keel, Moduli of surfaces with an anti-canonical cycle, Comp. Math Volume 151, Issue 2 (2015) , pp. 265-291.
[GTZ13] M. Gross, V. Tosatti, Y. Zhang, Collapsing of abelian fibered Calabi-Yau mani- folds, Duke Math. J., 162, (2013), no. 3, 517–551.
[GTZ16] M. Gross, V. Tosatti, Y. Zhang, Gromov-Hausdorff collapsing of Calabi-Yau manifolds, Comm. Anal. Geom. 24 (2016), no. 1, 93–113.
[Hart] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, Springer- Verlag.
[HaUe19] K.Hashimoto, K.Ueda, Reconstruction of general elliptic K3 surfaces from their Gromov- Hausdorff limits, Proce. A. M. S., Vol. 147, No. 5, 1963-1969, (2019).
[Hein12] H-J. Hein, Gravitational instantons from rational elliptic surfaces, J. Amer. Math. Soc. 25 (2012), 355-393
[HSVZ18] H.-J. Hein, S. Sun, J. Viaclovsky, R. Zhang, Nilpotent structures and collapsing Ricci-flat metrics on K3 surfaces, arXiv:1807.09367.
[HeTos15] H.-J. Hein, V. Tosatti, Remarks on the collapsing of torus fibered Calabi-Yau manifolds, Bull. Lond. Math. Soc. 47 (2015), no. 6, 1021–1027.
[HSZ19] S. Honda, S. Sun, R. Zhang, A note on the collapsing geometry of hyperKa¨hler four manifolds, Sci. China Math. 62, 2195-2210 (2019).
[Huy99] D. Huybrechts, Compact hyper-Ka¨hler manifolds: basic results, Invent. Math. 135 (1999), no. 1, 63–113.
[Huy01] D. Huybrechts, Compact HyperKa¨hler manifolds, in “Calabi-Yau Manifolds and Related Geometries” Lectures at a Summer School in Nordfjordeid, Norway, June 2001. Springer-Verlag (2001).
[Huy04] D. Huybrechts, Moduli spaces of hyperka¨hler manifolds and mirror symmetry. In Intersection theory and moduli, 185–247, ICTP Lect. Notes, XIX, Abdus Salam Int. Cent. Theoret. Phys., Trieste, (2004).
[Huy16] D. Huybrechts, Lectures on K3 surfaces, Cambridge Studies in Advanced Math- ematics, 158, Cambridge University Press (2016).
[Iit82] S. Iitaka, Algebraic Geometry – An Introduction to Birational Geometry of Alge- braic Varieties, Graduate Texts in Mathematics 76. Berlin: Springer, 1982.
[Kas77] A. Kas, Weierstrass normal forms and invariants of elliptic surfaces, Trans. Amer. Math. Soc, 225 (1977), 259-266.
[KeMo97] S.Keel, S.Mori, Quotients by groupoids, Ann. of Math. vol. 2, 145 (1), (1997), 193-213.
[Kob90a] R. Kobayashi, Moduli of Einstein metrics on a K3 Surface and degeneration of type I, In Ka¨hler Metrics and Moduli Spaces, 257–311, Adv. Stud. Pure Math., 18-II, T. Ochiai. ed. Academic Press, (1990).
[Kob90b] R. Kobayashi, Ricci-flat Ka¨hler metrics on aflne algebraic manifolds and de- generations of Ka¨hler-Einstein K3 surfaces, In Ka¨hler Metrics and Moduli Spaces, 257–311, Adv. Stud. Pure Math., 18-II, T. Ochiai. ed. Academic Press, (1990).
[Kod63] K. Kodaira, On compact analytic surfaces: II, Ann. of Math. 77 (1963), no. 3, 563-626.
[KolMor98] J. Kolla´r, S. Mori, Birational Geometry of Algebraic Varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, (1998).
[KS06] M. Kontsevich, Y. Soibelman, Aflne structures and non-archimedean analytic spaces, In The Unity of Mathematics, 321–385, Progr. Math., 244, Birkha¨user, 2006.
[Kon85] S. Kondo, Type II degeneration of K3 surfaces, Nagoya J. Math (1985) vol.99, 11-30.
[KP17] S. Kova´cs, Z. Patakfalvi, Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension, J. Amer. Math. Soc. 30 (2017), no. 4, 959-1021.
[LO19] R.Laza, K.OGrady, Birational geometry of the moduli space of quartic K3 sur- faces, Compositio Math. 155 (2019), no. 9, 1655-1710.
[LLL20] S-C.Liu, T-J.Lee, Y-S.Lee, On the complex aflne structures of SYZ fibration of Del Pezzo surfaces, arXiv:2005.04825.
[LM00] G. Laumon, L. Moret-Bailly, Champs Algebriques, Ergebnisse der Mathematik, Springer-Verlag Vol. 39 (2000).
[Looi76] E. Looijenga, Root sytems and elliptic curves, Invent. Math. 38, 17-32 (1976). [Luna73] D. Luna, Slices e´tales, Sur les groupes alge´briques, Bull. Soc. Math. France (1973).
[Manin] Y. Manin, Cubic forms, Algebra, Geometry, Arithmetic, Elsevier (1986). [McL98] R. McLean, Deformations of calibrated submanifolds, Comm. Anal. Geom. 6 (1998), 705–747.
[Mil] J. Milne, Algebraic Number theory, Lecture Notes. available at https://www.jmilne.org/math/CourseNotes/ANT210.pdf
[Mir81] R. Miranda, The moduli of Weierstrass fibrations over P1, Math. Ann. 255 (1981), no. 3, 379–394.
[Mum72b] D. Mumford, An analytic construction of degenerating abelian varieties over complete local rings, Compositio Math, vol. 24, no 3 (1972), 239-272.
[Mum77] D.Mumford, Hirzebruch’s proportionality theorem in the noncompact case, In- vent. Math. 42 (1), (1977), 239-272.
[Nik75] V.V. Nikulin, Kummer surfaces, Izv. Akad. Nauk SSSR Ser. Mat. 39 (1975), no. 2, 278–293, 471.
[Nik79] V.V. Nikulin, Integer symmetric bilinear forms and some of their geometric appli- cations, Izv. Akad. Nauk SSSR Ser. Mat. 43 (1999), no. 1, 111–177, 238.
[Od18a] Y. Odaka, Tropical Geometric Compactification of Moduli, I, - Mg case, Moduli of K-stable varieties, Springer INdAM series 31 (2018).
[Odk12a] Y. Odaka, The Calabi conjecture and K-stability, Int. Math. Res. Not. IMRN (2012), no. 10, 2272–2288.
[Odk12b] Y. Odaka, On the moduli of Ka¨hler-Einstein Fano manifolds, arXiv:1211.4833v4. Proceeding of Kinosaki algebraic geometry symposium 2013.
[Odk13a] Y. Odaka, The GIT stability of polarized varieties via Discrepancy, Ann. of Math. (2) 177 (2013), no. 2, 645–661.
[Odk13b] Y. Odaka, A generalization of the Ross-Thomas slope theory, Osaka J. Math. 50 (2013), no. 1, 171–185.
[Odk15] Y. Odaka, Compact moduli spaces of Ka¨hler-Einstein Fano varieties, Publ. Res. Int. Math. Sci. 51 (2015), no. 3, 549–565.
[Odk18] Y. Odaka, Tropical geometric compactification of Moduli, II - Ag case and holo- morphic limits -, Int. Math. Res. Not. 2018 (2018).
[OO18] Y. Odaka, Y. Oshima, Collapsing K3 surfaces and moduli compactification, Proc. Japan Acad. Ser. A Math. Sci. 94 (2018), no. 8, 81–86.
[OO21] Y. Odaka, Y. Oshima, Collapsing K3 surfaces, Tropical geometry and Moduli compactifications of Satake, Morgan-Shalen type, MSJ Memoir vol. 40, Math So- ciety of Japan (2021).
[OSS16] Y. Odaka, C. Spotti, S. Sun, Compact moduli spaces of del Pezzo surfaces and Ka¨hler-Einstein metrics, J. Differential Geom. 102 (2016), no. 1, 127–172.
[Od20a] Y.Odaka, Polystable log Calabi-Yau varieties and Gravitational instantons, arXiv:2009.13876.
[Od20b] Y.Odaka, Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures, arXiv:2011.12748.
[Od20c] Y.Odaka, On the K-stability and the moduli problem of varieties, Suugaku vol. 72, no.3 2020. (in Japanese).
[Osh] Y. Oshima, Collapsing Ricci-flat metrics for type II degeneration of K3 surfaces, in preparation.
[Ohno21] K. Ohno, Minimizing CM degree and slope stability of projective varieties, Math. Proc. Cambridge Phil. Soc., 1-13. (2021).
[PS21] J-Y.Park, J.Schmitt, Arithmetic Geometry of the moduli stack of Weierstrass fibra- tions over P1, arXiv:2107.12231.
[Pin77] H. C. Pinkham, Simple elliptic singularities, Del Pezzo surfaces and Cremona trans- formations, Several complex variables (Proc. Sympos. Pure Math., Vol. XXX, Part 1, Williams Coll., 1975), Amer. Math. Soc., Providence, R. I., 1977, pp. 69-71.
[Sei01] P.Seidel, More about vanishing cycles and mutation, Symplectic Geometry and Mirror Symmetry, Proceedings of the 4-th KIAS annual international conference (Seoul, 2000) K. Fukaya, Y.-G.Oh, K.Ono, G.Tian, eds. World Sci., 2001, 429-465.
[Sat56] I. Satake, On the compactification of the Siegel space, J. Indian Math. Soc. 20 (1956), 259–281.
[Sat60a] I. Satake, On representations and compactifications of symmetric Riemannian spaces, Ann. of Math. (2) 71 (1960), 77–110.
[Sat60b] I. Satake, On compactifications of the quotient spaces for arithmetically defined discontinuous groups, Ann. of Math. (2) 72 (1960), 555–580.
[Sca87] F. Scattone, On the compactification of moduli spaces for algebraic K3 surfaces, Mem. Amer. Math. Soc. 70 (1987), no. 374.
[Schm73] W. Schmid, Variation of Hodge structure: the singularities of the period map- ping, Invent. Math. 22 (1973), 211-319.
[Ser73] J.-P. Serre, A course in arithmetic, Graduate Texts in Mathematics, No. 7, Springer- Verlag (1973).
[Sha80] J. Shah, A complete moduli space for K3 surfaces of degree 2, Ann. of Math. (2) 112 (1980), no. 3, 485–510.
[Sha81] J. Shah, Degenerations of K3 surfaces of degree 4, Trans. Amer. Math. Soc. 263 (1981), no. 2, 271–308.
[She83] N.I. Shepherd-Barron, Degenerations with numerically effective canonical divi- sor, In The birational geometry of degenerations (Cambridge, Mass., 1981), 33–84, Progr. Math., vol. 29, Birkha¨user, Boston, (1983).
[She83] N.ShepherdBarron, Extending polarizations on families of K3 surfaces, (Cam- bridge, MA, 1981), Progr. Math vol 29, 135-171, Birkha¨user, Boston, 1983.
[Sil85] J.H.Silverman, The Arithmetic of Elliptic curves, Graduate Texts in Mathematics vol. 106 (1985)
[Shi05] T.Shioda, Elliptic surfaces and Davenport-Stothers triples, Comment. Math. Univ. St. Pauli 54 (2005), 49-68.
[Sto81] W.W.Stothers, Polynomial identities and Hauptmoduln, Quart. J. Math. Oxford (2) 32 (1981) 349-370.
[Take89] K. Takeuchi, Some birational maps of Fano 3-folds, Compositio Math., 71(3):265-283, 1989.
[TY90] G. Tian, S-T.Yau, Complete Ka¨hler manifolds with zero Ricci curvature I, J. Amer. Math. Sci., 3 (1990), 579-610.
[YZ96] S.T.Yau, E.Zaslow, BPS states, string duality, and nodal curves on K3, Nuclear Phys. B 471 (1996), 503-512.
[Zan95] U. Zannier, On Davenport’s bound for the degree of f 3 g2 and Riemann’s Exis- tence theorem, Acta Arithmetica LXXI.2 (1995).