Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Infinitesimal Torelli theorem for double coverings of surfaces of general type

Author: Igor Reider
Journal: J. Algebraic Geom. 14 (2005), 691-704
Published electronically: March 28, 2005
MathSciNet review: 2147352
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Abstract: Let $X$ be a smooth complex projective surface subject to the following conditions:

the canonical divisor $K_X$ of $X$ is ample,
the irregularity $q(X) = h^1(\mathcal{O}_X) =0$ and $p_g (X) =h^0 (\mathcal{O}_X (K_X)) \geq 2$,
the canonical linear system $\mid K_X\mid$ contains a reduced irreducible divisor.
It is shown that if $K^2_X \geq 5$, then the Infinitesimal Torelli theorem holds for a double covering of $X$ branched along a smooth divisor in the linear system $\mid 2K_X\mid$.

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Igor Reider
Affiliation: Université d’Angers, Département de Mathématiques, 2, Boulevard Lavoisier, 49045 Angers Cedex 01, France

Received by editor(s): July 13, 2004
Received by editor(s) in revised form: September 29, 2004
Published electronically: March 28, 2005