Vol. 3, No. 4, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 7, 1559–1821
Issue 6, 1311–1557
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Ideals generated by submaximal minors

Jan O. Kleppe and Rosa M. Miró-Roig

Vol. 3 (2009), No. 4, 367–392

The goal of this paper is to study irreducible families Wt,tt1(b¯;a¯) of codimension 4, arithmetically Gorenstein schemes X n defined by the submaximal minors of a t × t homogeneous matrix A whose entries are homogeneous forms of degree aj bi. Under some numerical assumption on aj and bi, we prove that the closure of Wt,tt1(b¯;a¯) is an irreducible component of Hilbp(x)(n), show that Hilbp(x)(n) is generically smooth along Wt,tt1(b¯;a¯), and compute the dimension of Wt,tt1(b¯;a¯) in terms of aj and bi. To achieve these results we first prove that X is determined by a regular section of Y Y 2(s) where s = deg(detA) and Y n is a codimension-2, arithmetically Cohen–Macaulay scheme defined by the maximal minors of the matrix obtained deleting a suitable row of A.

Hilbert scheme, arithmetically Gorenstein, determinantal schemes
Mathematical Subject Classification 2000
Primary: 14M12, 14C05, 14H10, 14J10
Secondary: 14N05
Received: 3 October 2007
Revised: 12 December 2008
Accepted: 12 December 2008
Published: 15 June 2009
Jan O. Kleppe
Oslo University College
Faculty of Engineering
Postboks 4, St. Olavs Plass
Oslo, N-0130
Rosa M. Miró-Roig
University of Barcelona
Algebra and Geometry
Gran Via de les Corts Catalanes 585
Barcelona, 08007