Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 2010 - Volume 53, Issue 01  

Research Article

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

Emmanuel Allauda1 and Javier Fernandeza2

a1 Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, USA, Email: (allaud@math.utah.edu)

a2 Instituto Balseiro, Universidad Nacional de Cuyo - CNEA, Bariloche R8402AGP, Argentina, Email: (jfernand@ib.edu.ar)

Abstract

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.

(Received January 30 2007)

Keywords

  • Hodge theory;
  • infinitesimal variations of Hodge structure;
  • geometric variation

2000 Mathematics subject classification

  • Primary 14D07;
  • Secondary 32G20