Stover
Matthew
en
2019-05-01
On general type surfaces with q=1 and c2=3pg
articles
https://link.springer.com/10.1007%2Fs00229-018-1035-y
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.
https://scigraph.springernature.com/explorer/license/
2019-04-11T14:20
research_article
1-12
false
2019-05
1432-1785
manuscripta mathematica
0025-2611
Mathematical Sciences
Springer Nature - SN SciGraph project
pub.1103792389
dimensions_id
bf4745616d643e8c153480e342d12f99881f6be86de0a1bbb0223eb2cee1d3bf
readcube_id
Temple University
Temple University, Philadelphia, USA
1-2
doi
10.1007/s00229-018-1035-y
Pure Mathematics
159