Publication Date

2008

Journal or Book Title

INTERNATIONAL MATHEMATICS RESEARCH NOTICES

Abstract

The Hard Lefschetz Theorem (HLT) and the Hodge–Riemann bilinear relations (HRR) hold in various contexts: they impose restrictions on the cohomology algebra of a smooth compact Kähler manifold; they restrict the local monodromy of a polarized variation of Hodge structure; they impose conditions on the f-vectors of convex polytopes. While the statements of these theorems depend on the choice of a Kähler class, or its analog, there is usually a cone of possible choices. It is then natural to ask whether the HLT and HRR remain true in a mixed context. In this note, we present a unified approach to proving the mixed HLT and HRR, generalizing the known results, and proving it in new cases, such as the intersection cohomology of nonrational polytopes.

Comments

This is the pre-published version harvested from ArXiv. The published version is located at http://imrn.oxfordjournals.org/content/2008/rnn025.refs

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