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The Classification of Regular Surfaces Isogenous to a Product of Curves with \(\chi ({\mathcal {O}}_S)= 2\)

  • Christian GleißnerEmail author
Conference paper
  • 501 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 123)

Abstract

A complex surface \(S\) is said to be isogenous to a product if \(S\) is a quotient \(S= (C_1 \times C_2)/G\) where the \(C_i\)’s are curves of genus at least two and \(G\) is a finite group acting freely on \(C_1 \times C_2\). In this article we classify all regular surfaces isogenous to a product with \(\chi (\mathcal O_S)=2\) under the assumption that the action of \(G\) is unmixed i.e. no element of \(G\) exchange the factors of the product \(C_1 \times C_2\).

Keywords

Surfaces Isogenous Unmixed Type Topological Euler Number Computer Algebra System Magma Perfect Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The author thanks Ingrid Bauer and Sascha Weigl for several suggestions, useful discussions and very careful reading of the paper.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Lehrstuhl Mathematik VIIIUniversität BayreuthBayreuthGermany

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