Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations
| dc.creator | Cattani, Eduardo | |
| dc.date | 2007-07-10 | |
| dc.date | 2008-02-19 | |
| dc.date.accessioned | 2026-07-07T09:21:20Z | |
| dc.date.available | 2026-07-07T09:21:20Z | |
| dc.description | Statements analogous to the Hard Lefschetz Theorem (HLT) and the Hodge-Riemann bilinear relations (HRR) hold in a variety of contexts: they impose restrictions on the cohomology algebra of a smooth compact Kähler manifold or on the intersection cohomology of a projective toric variety; they restrict the local monodromy of a polarized variation of Hodge structure; they impose conditions on the possible $f$-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 Kähler classes. 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 previously known results, and proving it in new cases such as the intersection cohomology of non-rational polytopes. | |
| dc.description | 13 pages - Minor revisions. Final version to appear in International Mathematics Research Notices | |
| dc.identifier | https://arxiv.org/abs/0707.1352 | |
| dc.identifier | http://arxiv.org/abs/0707.1352 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154986 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32G20 (Primary); 14F43, 32Q15, 52B20 (Secondary) | |
| dc.title | Mixed Lefschetz Theorems and Hodge-Riemann Bilinear Relations | |
| dc.type | text |