Combinatorial secant varieties

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The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal of the secant ideal coincides with the secant ideal of the initial ideal. For toric varieties, this leads to the notion of delightful triangulations of convex polytopes.
23 pages, 3 figures, The end of Section 5 has been rewritten

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Commutative Algebra, Algebraic Geometry, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/95104

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506223
 http://arxiv.org/abs/math/0506223

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arXiv