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Non-genericity of infinitesimal variations of Hodge structures arising in some geometric contexts

Part of: Deformations of analytic structures Families, fibrations

Published online by Cambridge University Press:  12 January 2010

Emmanuel Allaud  and
Javier Fernandez
Emmanuel Allaud
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, USA, Email: (allaud@math.utah.edu)
Javier Fernandez
Affiliation:
Instituto Balseiro, Universidad Nacional de Cuyo - CNEA, Bariloche R8402AGP, Argentina, Email: (jfernand@ib.edu.ar)
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Abstract

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We prove that the infinitesimal variations of Hodge structure arising in a number of geometric situations are non-generic. In particular, we consider the case of generic hypersurfaces in complete smooth projective toric varieties, generic hypersurfaces in weighted projective spaces and generic complete intersections in projective space and show that, for sufficiently high degrees, the corresponding infinitesimal variations are non-generic.

Keywords

Hodge theoryinfinitesimal variations of Hodge structuregeometric variation

MSC classification

Secondary: 14D07: Variation of Hodge structures 32G20: Period matrices, variation of Hodge structure; degenerations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 13 - 29
Copyright
Copyright © Edinburgh Mathematical Society 2010