Mixed Torelli problem for Todorov surfaces
type: Item
instance of: scholarly article
title: Mixed Torelli problem for Todorov surfaces
zbMATH Open document ID: 0774.14005
author: Sampei Usui
published in: Osaka Journal of Mathematics
publication date: 1992-09-27T00:00:00Z
review text: A projective surface \(X\) is a ` Todorov surface' when \(\chi({\mathcal O}_ X)=2\) and \(X\) is a double cover of a \(K3\) surface with only rational double points as singularities. For such surface, one can define a mixed Hodge structure on \(H^ 2(X-C)\) \((C=\) the unique effective canonical divisor) and then a mixed period map, so one is led to consider a Torelli problem for these surfaces. In this paper, an explicit construction of the mixed period map is described and the Torelli problem is studied by means of some `tame' degenerations of Todorov surfaces, to which the mixed period map can be extended. Using this procedure, the author gives a partial solution of the infinitesimal version of this Torelli problem.
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14C34
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14C30
zbMATH DE Number: 59715
zbMATH Keywords: cover of a \(K3\) surface
zbMATH Keywords: Todorov surface
zbMATH Keywords: mixed Hodge structure
zbMATH Keywords: mixed period map
zbMATH Keywords: Torelli problem
zbMATH Keywords: degenerations
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 59715