منابع مشابه
Hard Lefschetz theorem for simple polytopes
McMullen’s proof of the Hard Lefschetz Theorem for simple polytopes is studied, and a new proof of this theorem that uses conewise polynomial functions on a simplicial fan is provided.
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The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a gener...
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Techniques from algebraic geometry, in particular the hard Lefschetz theorem, are used to show that certain finite partially ordered sets O x derived from a class of algebraic varieties X have the k-Sperner property for all k. This in effect means that there is a simple description of the cardinality of the largest subset of C) x containing no (k + 1)-element chain. We analyze, in some detail, ...
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Contents 1. Introduction 1 2. Residue and tube over cycle maps 2 3. Hodge structures on the complement 8 4. Period maps and their derivatives 11 5. Tautological deformations of hypersurfaces 12 6. The main theorem 13 Appendix A. Spectral sequences 16 A.1. Fundamental Notions 16 A.2. Hypercohomology 24 A.3. Abstract de Rham theorems 26 A.4. The spectral sequence of a filtered complex of sheaves ...
متن کاملThe Noether-lefschetz Theorem
Earlier we defined the class group ClX of Weil divisors for an algebraic varietyX and the Cartier class group CaClX of Cartier divisors (which is isomorphic to the Picard group of isomorphism classes of line bundles with tensor product). These groups are isomorphic when X is smooth. In general it is quite difficult to compute these groups. In this section we will give some classic examples with...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2019
ISSN: 0001-8708
DOI: 10.1016/j.aim.2019.03.006