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

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00229-018-1035-y

DOI

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

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1103792389


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