Algebra & Number Theory
- Algebra Number Theory
- Volume 3, Number 4 (2009), 367-392.
Ideals generated by submaximal minors
The goal of this paper is to study irreducible families of codimension 4, arithmetically Gorenstein schemes defined by the submaximal minors of a homogeneous matrix whose entries are homogeneous forms of degree . Under some numerical assumption on and , we prove that the closure of is an irreducible component of , show that is generically smooth along , and compute the dimension of in terms of and . To achieve these results we first prove that is determined by a regular section of where and is a codimension-2, arithmetically Cohen–Macaulay scheme defined by the maximal minors of the matrix obtained deleting a suitable row of .
Algebra Number Theory, Volume 3, Number 4 (2009), 367-392.
Received: 3 October 2007
Revised: 12 December 2008
Accepted: 12 December 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14M12: Determinantal varieties [See also 13C40] 14C05: Parametrization (Chow and Hilbert schemes) 14H10: Families, moduli (algebraic) 14J10: Families, moduli, classification: algebraic theory
Secondary: 14N05: Projective techniques [See also 51N35]
Kleppe, Jan; Miró-Roig, Rosa. Ideals generated by submaximal minors. Algebra Number Theory 3 (2009), no. 4, 367--392. doi:10.2140/ant.2009.3.367. https://projecteuclid.org/euclid.ant/1513797417