Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space

Details Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space

2009-11-07

arxiv.org/abs/0911.1466v2

Mathematics

Algebraic Geometry

26 pages, 1 figure, article dedicated to David Mumford on the occasion of his 2^3 . 3^2-th birthday

Scientific paper

We prove in one go that each of the 4 families of Burniat surfaces with K^2 = 6,5,4, is a connected component of the moduli space of surfaces of general type. We prove also the rationality of each component. In the nodal case (one of the two families for K^2_S = 4) a very surprising and new phenomenon occurs. Both the moduli space for the minimal models and the Gieseker moduli space for canonical models are everywhere non reduced. But the nilpotence order is higher for the first.

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