Combinatorial secant varieties

Details Combinatorial secant varieties Combinatorial secant varieties

2005-06-12

arxiv.org/abs/math/0506223v3

Mathematics

Commutative Algebra

23 pages, 3 figures, The end of Section 5 has been rewritten

Scientific paper

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.

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