Combinatorial secant varieties
交换代数
2007-05-23 v3 代数几何
组合数学
摘要
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.
引用
@article{arxiv.math/0506223,
title = {Combinatorial secant varieties},
author = {Bernd Sturmfels and Seth Sullivant},
journal= {arXiv preprint arXiv:math/0506223},
year = {2007}
}
备注
23 pages, 3 figures, The end of Section 5 has been rewritten