Mixed ladder determinantal varieties from two-sided ladders
Commutative Algebra
2007-05-23 v3 Algebraic Geometry
Abstract
We study the family of ideals defined by mixed size minors of two-sided ladders of indeterminates. We compute their Groebner bases with respect to a skew-diagonal monomial order, then we use them to compute the height of the ideals. We show that these ideals correspond to a family of irreducible projective varieties, that we call mixed ladder determinantal varieties. We show that these varieties are arithmetically Cohen-Macaulay. We characterize the arithmetically Gorenstein ones, among those that satisfy a technical condition. Our main result consists in proving that mixed ladder determinantal varieties belong to the same G-biliaison class of a linear variety.
Cite
@article{arxiv.math/0510529,
title = {Mixed ladder determinantal varieties from two-sided ladders},
author = {Elisa Gorla},
journal= {arXiv preprint arXiv:math/0510529},
year = {2007}
}
Comments
15 pages, contains an improved version of Theorem 1.25 (now 1.23)