A motivic study of generalized Burniat surfaces

2017/10/06 by Chris Peters, Peters, Chris
Mathematics · #14C15 #14C25 #14C30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C15 #msc:14C25 #msc:14C30

paper · pdf · doi:10.48550/arxiv.1710.02370

arxiv created 2017/10/06 · arxiv updated 2017/10/09

Abstract

Generalized Burniat surfaces are surfaces of general type with p_g=q and Euler number e=6 obtained by a variant of Inoue's construction method for the classical Burniat surfaces. I prove a variant of the Bloch conjecture for these surfaces. The method applies also to the so-called Sicilian surfaces introduced by Bauer, Catanese and Frapporti. This implies that the Chow motives of all of these surfaces are finite-dimensional in the sense of Kimura.

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