On general type surfaces with q=1 and c2=3pg View Full Text


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Article Info

DATE

2019-05

AUTHORS

Matthew Stover

ABSTRACT

Let S be a minimal surface of general type with irregularity q(S)=1. Well-known inequalities between characteristic numbers imply that 3pg(S)≤c2(S)≤10pg(S),where pg(S) is the geometric genus and c2(S) the topological Euler characteristic. Surfaces achieving equality for the upper bound are classified, starting with work of Debarre. We study equality in the lower bound, showing that for each n≥1 there exists a surface with q=1, pg=n, and c2=3n. The moduli space Mn of such surfaces is a finite set of points, and we prove that #Mn→∞ as n→∞. Equivalently, this paper studies the number of closed complex hyperbolic 2-manifolds of first betti number 2 as a function of volume; in particular, such a manifold exists for every possible volume. More... »

PAGES

1-12

References to SciGraph publications

  • 2006. Complex Surfaces of General Type: Some Recent Progress in GLOBAL ASPECTS OF COMPLEX GEOMETRY
  • 1989-12. Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups in PUBLICATIONS MATHÉMATIQUES DE L'IHÉS
  • 2014-10. Hurwitz ball quotients in MATHEMATISCHE ZEITSCHRIFT
  • 2015-12. On asymptotic bounds for the number of irreducible components of the moduli space of surfaces of general type in RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO SERIES 2
  • 2003. Subgroup Growth in NONE
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    http://scigraph.springernature.com/pub.10.1007/s00229-018-1035-y

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    http://dx.doi.org/10.1007/s00229-018-1035-y

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