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MIXED QUASI-ÉTALE QUOTIENTS WITH ARBITRARY SINGULARITIES

Published online by Cambridge University Press:  26 August 2014

DAVIDE FRAPPORTI  and
ROBERTO PIGNATELLI
DAVIDE FRAPPORTI
Affiliation:
University of Bayreuth, Lehrstuhl Mathematik VIII, Universitaetsstrasse 30, D-95447 Bayreuth, Germany e-mail: Davide.Frapporti@uni-bayreuth.de
ROBERTO PIGNATELLI
Affiliation:
Dipartimento di Matematica, Università di Trento, Via Sommarive 14, I-38123 Trento, Italy e-mail: Roberto.Pignatelli@unitn.it
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Abstract

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A mixed quasi-étale quotient is the quotient of the product of a curve of genus at least 2 with itself by the action of a group which exchanges the two factors and acts freely outside a finite subset. A mixed quasi-étale surface is the minimal resolution of its singularities. We produce an algorithm computing all mixed quasi-étale surfaces with given geometric genus, irregularity and self-intersection of the canonical class. We prove that all irregular mixed quasi-étale surfaces of general type are minimal. As an application, we classify all irregular mixed quasi-étale surfaces of general type with genus equal to the irregularity, and all the regular ones with K2 > 0, thus constructing new examples of surfaces of general type with χ = 1. We mention the first example of a minimal surface of general type with pg = q = 1 and Albanese fibre of genus bigger than K2.

Keywords

14J2958E4014Q10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 57 , Issue 1 , January 2015 , pp. 143 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 2014 

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