On Semi-isogenous Mixed Surfaces

Let C be a compact Riemann surface. Let us consider a finite group acting on CxC, having some elements that exchange the factors, and assume that the subgroup of those elements that do not exchange the factors acts freely. We call the quotient a Semi-isogenous Mixed Surface. In this work we investigate these surfaces and we explain how their geometry is encoded in the group. Based on this, we present an algorithm to classify the Semi-isogenous Mixed Surfaces with given geometric genus, irregularity and self-intersection of the canonical class. In particular we give the classification of Semi-isogenous Mixed Surfaces with K^2>0 and holomorphic Euler-Poincaré characteristic equal to 1, where new examples of minimal surfaces of general type appear. Minimality of Semi-isogenous Mixed Surfaces is discussed using two different approaches. The first one involves the study of the bicanonical system of such surfaces: we prove that we can relate the dimension of its first cohomology group to the rank of a linear map that involves only curves. The second approach exploits Hodge index theorem to bound the number of exceptional curves that live on a Semi-isogenous Mixed Surface.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2017

Author dc:creator

• Cancian, Nicola

Contributors dc:contributor

• Pignatelli, Roberto

• Settore MAT/03 - Geometria

Statement dc:rights

• info:eu-repo/semantics/closedAccess
• license:Tutti i diritti riservati (All rights reserved)

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_369295
10.15168/11572_369295

OAI identifier oai:identifier

oai:iris.unitn.it:11572/369295