Ideals generated by submaximal minors

Author(s)

Publication date

2009

Series/Report no

Algebra & Number Theory;3 (4)

Publisher

Mathematical Science Publishers

Document type

Abstract

The goal of this paper is to study irreducible families W(b;a) of codimension 4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minors of a t x t matrix A whose entries are homogeneous forms of degree a_j-b_i. Under some numerical assumption on a_j and b_i we prove that the closure of W(b;a) is an irreducible component of Hilb^p(P^n), we show that Hilb^p(P^n) is generically smooth along W(b;a) and we compute the dimension of W(b;a) in terms of a_j and b_i. To achieve these results we first prove that X is determined by a regular section of the twisted conormal sheaf I_Y/I^2_Y(s) where s=deg(det(A)) and Y is a codimension 2, arithmetically Cohen-Macaulay scheme of P^n defined by the maximal minors of the matrix obtained deleting a suitable row of A.

Keywords

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Originally published by the Mathematical Science Publishers (http://mathscipub.org/)

Permanent URL (for citation purposes)

  • http://hdl.handle.net/10642/385