Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space
Algebraic Geometry
2015-05-14 v2
Abstract
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.
Cite
@article{arxiv.0911.1466,
title = {Burniat surfaces II: secondary Burniat surfaces form three connected components of the moduli space},
author = {Ingrid Bauer and Fabrizio Catanese},
journal= {arXiv preprint arXiv:0911.1466},
year = {2015}
}
Comments
26 pages, 1 figure, article dedicated to David Mumford on the occasion of his 2^3 . 3^2-th birthday