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Compact moduli of elliptic K3 surfaces

Kenneth Ascher and Dori Bejleri

Geometry & Topology 27 (2023) 1891–1946
Bibliography
1 D Abramovich, A Vistoli, Complete moduli for fibered surfaces, from: "Recent progress in intersection theory" (editors G Ellingsrud, W Fulton, A Vistoli), Birkhäuser (2000) 1 MR1849290
2 D Abramovich, A Vistoli, Compactifying the space of stable maps, J. Amer. Math. Soc. 15 (2002) 27 MR1862797
3 V Alexeev, Boundedness and K2 for log surfaces, Internat. J. Math. 5 (1994) 779 MR1298994
4 V Alexeev, A Brunyate, P Engel, Compactifications of moduli of elliptic K3 surfaces : stable pair and toroidal, Geom. Topol. 26 (2022) 3525 MR4562567
5 V Alexeev, P Engel, A Thompson, Stable pair compactification of moduli of K3 surfaces of degree 2, J. Reine Angew. Math. 799 (2023) 1 MR4595306
6 K Ascher, D Bejleri, Log canonical models of elliptic surfaces, Adv. Math. 320 (2017) 210 MR3709104
7 K Ascher, D Bejleri, Moduli of fibered surface pairs from twisted stable maps, Math. Ann. 374 (2019) 1007 MR3961332
8 K Ascher, D Bejleri, Moduli of weighted stable elliptic surfaces and invariance of log plurigenera, Proc. Lond. Math. Soc. 122 (2021) 617 MR4258169
9 K Ascher, D Bejleri, Smoothability of relative stable maps to stacky curves, Épijournal Géom. Algébrique 7 (2023) MR4545361
10 W L Baily Jr., A Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966) 442 MR216035
11 W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
12 A Brunyate, A modular compactification of the space of elliptic K3 surfaces, PhD thesis, University of Georgia (2015)
13 C Cadman, Using stacks to impose tangency conditions on curves, Amer. J. Math. 129 (2007) 405 MR2306040
14 I V Dolgachev, Mirror symmetry for lattice polarized K3 surfaces, J. Math. Sci. 81 (1996) 2599 MR1420220
15 R Friedman, A new proof of the global Torelli theorem for K3 surfaces, Ann. of Math. 120 (1984) 237 MR763907
16 R Friedman, The period map at the boundary of moduli, from: "Topics in transcendental algebraic geometry" (editor P Griffiths), Ann. of Math. Stud. 106, Princeton Univ. Press (1984) 183 MR756852
17 A Gathmann, Absolute and relative Gromov–Witten invariants of very ample hypersurfaces, Duke Math. J. 115 (2002) 171 MR1944571
18 N Giansiracusa, W D Gillam, On Kapranov’s description of M0,n as a Chow quotient, Turkish J. Math. 38 (2014) 625 MR3195733
19 C D Hacon, J McKernan, C Xu, Boundedness of moduli of varieties of general type, J. Eur. Math. Soc. 20 (2018) 865 MR3779687
20 C D Hacon, C Xu, Existence of log canonical closures, Invent. Math. 192 (2013) 161 MR3032329
21 A Harder, A Thompson, The geometry and moduli of K3 surfaces, from: "Calabi–Yau varieties : arithmetic, geometry and physics" (editors R Laza, M Schütt, N Yui), Fields Inst. Monogr. 34, Fields Inst. Res. Math. Sci. (2015) 3 MR3409771
22 R Hartshorne, C Polini, Divisor class groups of singular surfaces, Trans. Amer. Math. Soc. 367 (2015) 6357 MR3356940
23 B Hassett, Moduli spaces of weighted pointed stable curves, Adv. Math. 173 (2003) 316 MR1957831
24 G Heckman, E Looijenga, The moduli space of rational elliptic surfaces, from: "Algebraic geometry 2000" (editors S Usui, M Green, L Illusie, K Kato, E Looijenga, S Mukai, S Saito), Adv. Stud. Pure Math. 36, Math. Soc. Japan (2002) 185 MR1971517
25 G Inchiostro, Moduli of Weierstrass fibrations with marked section, Adv. Math. 375 (2020) 107374 MR4137071
26 J Kollár, Singularities of the minimal model program, 200, Cambridge Univ. Press (2013) MR3057950
27 J Kollár, Mumford’s influence on the moduli theory of algebraic varieties, Pure Appl. Math. Q. 17 (2021) 619 MR4257596
28 J Kollár, Families of varieties of general type, (2022)
29 J Kollár, S J Kovács, Log canonical singularities are Du Bois, J. Amer. Math. Soc. 23 (2010) 791 MR2629988
30 J Kollár, S Mori, Birational geometry of algebraic varieties, 134, Cambridge Univ. Press (1998) MR1658959
31 J Kollár, N I Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988) 299 MR922803
32 S J Kovács, Z Patakfalvi, Projectivity of the moduli space of stable log-varieties and subadditivity of log-Kodaira dimension, J. Amer. Math. Soc. 30 (2017) 959 MR3671934
33 G La Nave, Explicit stable models of elliptic surfaces with sections, preprint (2002) arXiv:math/0205035
34 R Laza, The KSBA compactification for the moduli space of degree two K3 pairs, J. Eur. Math. Soc. 18 (2016) 225 MR3459951
35 R Laza, Z Zhang, Classical period domains, from: "Recent advances in Hodge theory" (editors M Kerr, G Pearlstein), London Math. Soc. Lecture Note Ser. 427, Cambridge Univ. Press (2016) 3 MR3409869
36 R Miranda, The moduli of Weierstrass fibrations over 1, Math. Ann. 255 (1981) 379 MR615858
37 R Miranda, The basic theory of elliptic surfaces, ETS Editrice (1989) MR1078016
38 V V Nikulin, Finite groups of automorphisms of Kählerian K3 surfaces, Trudy Moskov. Mat. Obshch. 38 (1979) 75 MR544937
39 Y Odaka, Y Oshima, Collapsing K3 surfaces, tropical geometry and moduli compactifications of Satake, Morgan–Shalen type, 40, Math. Soc. Japan (2021) MR4290084
40 M C Olsson, (Log) twisted curves, Compos. Math. 143 (2007) 476 MR2309994
41 U Persson, Configurations of Kodaira fibers on rational elliptic surfaces, Math. Z. 205 (1990) 1 MR1069483
42 F Scattone, On the compactification of moduli spaces for algebraic K3 surfaces, 374, Amer. Math. Soc. (1987) MR912636
43 M Schütt, T Shioda, Elliptic surfaces, from: "Algebraic geometry in East Asia" (editors J Keum, S Kondō, K Konno, K Oguiso), Adv. Stud. Pure Math. 60, Math. Soc. Japan (2010) 51 MR2732092
44 T Shioda, The elliptic K3 surfaces with a maximal singular fibre, C. R. Math. Acad. Sci. Paris 337 (2003) 461 MR2023754
45 R Vakil, The enumerative geometry of rational and elliptic curves in projective space, J. Reine Angew. Math. 529 (2000) 101 MR1799935