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

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.

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

References in corpus (2)

• Quotients of products of curves, new surfaces with $p_g=0$ and their fundamental groups
• Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces

Cited by in corpus (10)

• A Superficial Working Guide to Deformations and Moduli
• Generalized Burniat type surfaces and Bagnera-de Franchis varieties
• Kulikov surfaces form a connected component of the moduli space
• The compactifications of moduli spaces of Burniat surfaces with $2\le K^2\le 5$
• Surfaces with $p_g=0$, $K^2=5$ and bicanonical maps of degree 4
• Unprojection and deformations of tertiary Burniat surfaces
• Commuting involutions on surfaces of general type with p_g=0 and K^2=7
• Burniat-type surfaces and a new family of surfaces with p_g = 0, K^2 = 3
• Surfaces with p_g = 0: Constructions and Moduli spaces, Burniat surfaces and deformations of automorphisms
• A characterization of Burniat surfaces with $K^2=4$ and of non nodal type