The G-biliaison class of symmetric determinantal schemes

Details The G-biliaison class of symmetric determinantal schemes The G-biliaison class of symmetric determinantal schemes

2005-05-19

arxiv.org/abs/math/0505414v4

Mathematics

Algebraic Geometry

20 pages, reference addeded, a few mistakes fixed, final version to appear on J. Algebra

Scientific paper

We consider a family of schemes, that are defined by minors of a homogeneous symmetric matrix with polynomial entries. We assume that they have maximal possible codimension, given the size of the matrix and of the minors that define them. We show that these schemes are G-bilinked to a linear variety of the same dimension. In particular, they can be obtained from a linear variety by a finite sequence of ascending G-biliaisons on some determinantal schemes. In particular, it follows that these schemes are glicci. We describe the biliaisons explicitely in the proof of the main theorem.

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