Volume 19, issue 4 (2015)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 7, 3001–3510
Issue 6, 2483–2999
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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