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Burniat-type surfaces and a new family of surfaces with \(p_g = 0, K^2=3\)

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Abstract

The paper is one of a series devoted to the classification, the moduli spaces and the classification of surfaces of general type with \(p_g=0\). Here we generalize a classical construction due to P. Burniat (revised by M. Inoue). Among other results we construct a family of surfaces of general type with \(K_S^2 = 3\), \(p_g(S) = 0\) realizing a new fundamental group of order 16.

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Notes

  1. Unlike other authors, when we write ‘fundamental group’, we mean the topological fundamental group, and not its profinite completion, the algebraic fundamental group.

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Authors and Affiliations

  1. Lehrstuhl Mathematik VIII, Mathematisches Institut, Universität Bayreuth, NW II, Universitätsstr. 30, 95447,  Bayreuth, Germany

    I. Bauer & F. Catanese

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  1. I. Bauer
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  2. F. Catanese
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Correspondence to I. Bauer.

Additional information

The present work took place in the realm of the DFG Forschergruppe 790 “Classification of algebraic surfaces and compact complex manifolds”. A large part of this work was done while the authors were guests at KIAS, Seoul in April 2012: we are grateful to KIAS for the hospitality and wonderful working environment.

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Bauer, I., Catanese, F. Burniat-type surfaces and a new family of surfaces with \(p_g = 0, K^2=3\) . Rend. Circ. Mat. Palermo 62, 37–60 (2013). https://doi.org/10.1007/s12215-013-0108-8

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