Geometry & Topology Volume 22, issue 4 (2018)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Classification and arithmeticity of toroidal compactifications with $3\bar{c}_2 = \bar{c}_1^{\mskip2mu 2} = 3$

Luca F Di Cerbo and Matthew Stover

Geometry & Topology 22 (2018) 2465–2510

DOI: 10.2140/gt.2018.22.2465

Bibliography

1	A Ash, D Mumford, M Rapoport, Y S Tai, Smooth compactifications of locally symmetric varieties, Cambridge Univ. Press (2010) MR2590897
2	G Bagnera, M d Franchis, Sur les surfaces hyperelliptiques, C. R. Acad. Sci. Paris 145 (1908) 747
3	W P Barth, K Hulek, C A M Peters, A Van de Ven, Compact complex surfaces, 4, Springer (2004) MR2030225
4	I Bauer, F Catanese, R Pignatelli, Surfaces of general type with geometric genus zero: a survey, from: "Complex and differential geometry" (editors W Ebeling, K Hulek, K Smoczyk), Springer Proc. Math. 8, Springer (2011) 1 MR2964466
5	A Beauville, Complex algebraic surfaces, 34, Cambridge Univ. Press (1996) MR1406314
6	M Belolipetsky, Hyperbolic orbifolds of small volume, from: "Proceedings of the International Congress of Mathematicians, II : Invited lectures" (editors S Y Jang, Y R Kim, D W Lee, I Yie), Kyung Moon Sa (2014) 837
7	A Borel, L Ji, Compactifications of symmetric and locally symmetric spaces, 229, Birkhäuser (2006) MR2189882
8	W Bosma, J Cannon, C Playoust, The Magma algebra system, I : The user language, J. Symbolic Comput. 24 (1997) 235 MR1484478
9	D I Cartwright, T Steger, Enumeration of the 50 fake projective planes, C. R. Math. Acad. Sci. Paris 348 (2010) 11 MR2586735
10	O Debarre, Tores et variétés abéliennes complexes, 6, Soc. Math. France (1999) MR1767634
11	P Deligne, G D Mostow, Commensurabilities among lattices in PU(1,n), 132, Princeton Univ. Press (1993) MR1241644
12	G Di Cerbo, L F Di Cerbo, Effective results for complex hyperbolic manifolds, J. Lond. Math. Soc. 91 (2015) 89 MR3338610
13	L F Di Cerbo, Finite-volume complex-hyperbolic surfaces, their toroidal compactifications, and geometric applications, Pacific J. Math. 255 (2012) 305 MR2928554
14	L F Di Cerbo, On the classification of toroidal compactifications with 3c₂ = c₁² and c₂ = 1, preprint (2014) arXiv:1309.5516v3
15	L F Di Cerbo, M Stover, Multiple realizations of varieties as ball quotient compactifications, Michigan Math. J. 65 (2016) 441 MR3510915
16	L F Di Cerbo, M Stover, Bielliptic ball quotient compactifications and lattices in PU(2,1) with finitely generated commutator subgroup, Ann. Inst. Fourier (Grenoble) 67 (2017) 315 MR3612333
17	E Falbel, J R Parker, The geometry of the Eisenstein–Picard modular group, Duke Math. J. 131 (2006) 249 MR2219242
18	R Friedman, Algebraic surfaces and holomorphic vector bundles, Springer (1998) MR1600388
19	D Gabai, R Meyerhoff, P Milley, Minimum volume cusped hyperbolic three-manifolds, J. Amer. Math. Soc. 22 (2009) 1157 MR2525782
20	M Gromov, Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982) 5 MR686042
21	R Hartshorne, Algebraic geometry, 52, Springer (1977) MR0463157
22	F Hirzebruch, Chern numbers of algebraic surfaces: an example, Math. Ann. 266 (1984) 351 MR730175
23	R P Holzapfel, Chern numbers of algebraic surfaces—Hirzebruch’s examples are Picard modular surfaces, Math. Nachr. 126 (1986) 255 MR846579
24	R P Holzapfel, Ball and surface arithmetics, 29, Vieweg (1998) MR1685419
25	R P Holzapfel, Complex hyperbolic surfaces of abelian type, Serdica Math. J. 30 (2004) 207 MR2098333
26	C Hummel, Rank one lattices whose parabolic isometries have no rotational part, Proc. Amer. Math. Soc. 126 (1998) 2453 MR1443390
27	Y Kawamata, On deformations of compactifiable complex manifolds, Math. Ann. 235 (1978) 247 MR499279
28	B Klingler, Sur la rigidité de certains groupes fondamentaux, l’arithméticité des réseaux hyperboliques complexes, et les “faux plans projectifs”, Invent. Math. 153 (2003) 105 MR1990668
29	Y Miyaoka, On the Chern numbers of surfaces of general type, Invent. Math. 42 (1977) 225 MR0460343
30	N Mok, Projective algebraicity of minimal compactifications of complex-hyperbolic space forms of finite volume, from: "Perspectives in analysis, geometry, and topology" (editors I Itenberg, B Jöricke, M Passare), Progr. Math. 296, Springer (2012) 331 MR2884042
31	A Momot, Irregular ball-quotient surfaces with non-positive Kodaira dimension, Math. Res. Lett. 15 (2008) 1187 MR2470393
32	D Mumford, Hirzebruch’s proportionality theorem in the noncompact case, Invent. Math. 42 (1977) 239 MR471627
33	D Mumford, An algebraic surface with K ample, (K²) = 9, p_g = q = 0, Amer. J. Math. 101 (1979) 233 MR527834
34	G Prasad, S K Yeung, Fake projective planes, Invent. Math. 168 (2007) 321 MR2289867
35	F Sakai, Semistable curves on algebraic surfaces and logarithmic pluricanonical maps, Math. Ann. 254 (1980) 89 MR597076
36	F Serrano, Divisors of bielliptic surfaces and embeddings in P⁴, Math. Z. 203 (1990) 527 MR1038716
37	M Stover, Volumes of Picard modular surfaces, Proc. Amer. Math. Soc. 139 (2011) 3045 MR2811261
38	G Tian, S T Yau, Existence of Kähler–Einstein metrics on complete Kähler manifolds and their applications to algebraic geometry, from: "Mathematical aspects of string theory" (editor S T Yau), Adv. Ser. Math. Phys. 1, World Scientific (1987) 574 MR915840
39	G Urzúa, Arrangements of curves and algebraic surfaces, J. Algebraic Geom. 19 (2010) 335 MR2580678
40	S T Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge–Ampère equation, I, Comm. Pure Appl. Math. 31 (1978) 339 MR480350
41	S K Yeung, Integrality and arithmeticity of co-compact lattice corresponding to certain complex two-ball quotients of Picard number one, Asian J. Math. 8 (2004) 107 MR2128300