Generic Torelli Theorem for Hypersurfaces in Compact Irreducible Hermitian Symmetric Spaces

Abstract

This chapter discusses Generic Torelli theorem for hypersurfaces in compact irreducible Hermitian Symmetric spaces. It focuses on hypersurfaces of degree ≥ 3 in compact irreducible Hermitian symmetric spaces Y. Such symmetric spaces are classified into six classes. The ingredients of the proof of generic Torelli theorem in the projective case are as follows: (1) an interpretation of the IVHS of smooth hypersurfaces by means of their Jacobian rings, (2) a symmetrizer lemma, (3) the polynomial structure (the defining ideal of the Veronese embedding of PN). The chapter discusses the vanishing theorem, construction of Kahler C-spaces, homogeneous vector bundles and the compact irreducible Hermitian symmetric spaces. It also discusses Kostant's decomposition of ΩPY and the properties of weights and roots of G.