Mixed Torelli problem for Todorov surfaces (Q1191276)

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.