- 443256.pdf (1M)

## 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

## Version

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

## Permanent URL (for citation purposes)

- http://hdl.handle.net/10642/385