Volume 19, issue 4 (2015)

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Varieties of general type with the same Betti numbers as $\mathbb{P}^1\times \mathbb{P}^1\times\cdots\times \mathbb{P}^1$

Amir Džambić

Geometry & Topology 19 (2015) 2257–2276
Bibliography
1 I C Bauer, F Catanese, F Grunewald, The classification of surfaces with $p_g=q=0$ isogenous to a product of curves, Pure Appl. Math. Q. 4 (2008) 547 MR2400886
2 K Belabas, J Buchmann, H Cohen, F Diaz y Diaz, D Ford, P Létard, M Olivier, M Pohst, A Schwarz, Tables of number fields
3 M Belolipetsky, B Linowitz, On fields of definition of arithmetic Kleinian reflection groups, II, Int. Math. Res. Not. 2014 (2014) 2559 MR3207375
4 A Borel, Commensurability classes and volumes of hyperbolic $3$–manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 8 (1981) 1 MR616899
5 K S Brown, Cohomology of groups, Graduate Texts in Math. 87, Springer (1982) MR672956
6 F Catanese, Fibred surfaces, varieties isogenous to a product and related moduli spaces, Amer. J. Math. 122 (2000) 1 MR1737256
7 T Chinburg, E Friedman, The smallest arithmetic hyperbolic three-orbifold, Invent. Math. 86 (1986) 507 MR860679
8 A Džambić, Fake quadrics from irreducible lattices acting on the product of upper half planes, Math. Ann. 360 (2014) 23 MR3263157
9 F Hirzebruch, Automorphe Formen und der Satz von Riemann–Roch, from: "Symposium internacional de topología algebraica International symposium on algebraic topology", Universidad Nacional Autónoma de México and UNESCO (1958) 129 MR0103280
10 F Hirzebruch, Gesammelte Abhandlungen, Vol. I, Springer (1987) 1951 MR931775
11 C Maclachlan, A W Reid, The arithmetic of hyperbolic $3$–manifolds, Graduate Texts in Math. 219, Springer (2003) MR1937957
12 Y Matsushima, G Shimura, On the cohomology groups attached to certain vector valued differential forms on the product of the upper half planes, Ann. of Math. 78 (1963) 417 MR0155340
13 J Neukirch, Algebraic number theory, Grundl. Math. Wissen. 322, Springer (1999) MR1697859
14 A Odlyzko, Discriminant bounds, tables of calculations (1976)
15 G Prasad, S K Yeung, Fake projective planes, Invent. Math. 168 (2007) 321 MR2289867
16 G Prasad, S K Yeung, Arithmetic fake projective spaces and arithmetic fake Grassmannians, Amer. J. Math. 131 (2009) 379 MR2503987
17 G Prasad, S K Yeung, Addendum to “Fake projective planes” Invent. Math. 168 (2007) 321–370, Invent. Math. 182 (2010) 213 MR2672284
18 G Prasad, S K Yeung, Nonexistence of arithmetic fake compact Hermitian symmetric spaces of type other than $A_n$ $(n\leq 4)$, J. Math. Soc. Japan 64 (2012) 683 MR2965425
19 I H Shavel, A class of algebraic surfaces of general type constructed from quaternion algebras, Pacific J. Math. 76 (1978) 221 MR0572981
20 G Shimura, Construction of class fields and zeta functions of algebraic curves, Ann. of Math. 85 (1967) 58 MR0204426
21 C L Siegel, Berechnung von Zetafunktionen an ganzzahligen Stellen, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II 1969 (1969) 87 MR0252349
22 M F Vignéras, Invariants numériques des groupes de Hilbert, Math. Ann. 224 (1976) 189 MR0429755
23 M F Vignéras, Arithmétique des algèbres de quaternions, Lecture Notes in Math. 800, Springer (1980) MR580949
24 J Voight, Enumeration of totally real number fields of bounded root discriminant, from: "Algorithmic number theory" (editors A J van der Poorten, A Stein), Lecture Notes in Comput. Sci. 5011, Springer (2008) 268 MR2467853
25 J Voight, Tables of totally real number fields, tables of calculations (2012)
26 L C Washington, Introduction to cyclotomic fields, Graduate Texts in Math. 83, Springer (1997) MR1421575
27 R Zimmert, Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung, Invent. Math. 62 (1981) 367 MR604833