Erratum to Burniat surfaces II secondary Burniat

Authors: I Bauer F Catanese

Publish Date: 2014/06/03

Volume: 197, Issue: 1, Pages: 237-240

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Abstract

The main goal of this note is to correct an erroneous statement in the originally published article nodal Burniat surfaces with K2 S = 4 do not form a connected component of the moduli space but are properly contained in a unique irreducible connected component Therefore the title should be amended to ‘Secondary Burniat surfaces yield three connected components of the moduli space’The subset of the moduli space of canonical surfaces of general type mathfrak Mcan 14 given by the union of the open set corresponding to extended Burniat surfaces with K2 S = 4 with the irreducible closed set parametrizing nodal Burniat surfaces with K2 S = 4 is an irreducible connected component normal unirational of dimension 3Details and proofs of the amended statements can be found in 1 in particular the complicated definition of extended Burniat surfaces It may suffice here to say that these are birational to bidouble covers ie Galois covers with group mathbb Z/22 of the plane with branch divisors consisting of lines and one conic as in the picture above

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