Mixed ladder determinantal varieties from two-sided ladders

Details Mixed ladder determinantal varieties from two-sided ladders Mixed ladder determinantal varieties from two-sided ladders

2005-10-25

arxiv.org/abs/math/0510529v3

Mathematics

Commutative Algebra

15 pages, contains an improved version of Theorem 1.25 (now 1.23)

Scientific paper

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.

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