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Proceedings of the American Mathematical Society

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Families of determinantal schemes


Authors: Jan O. Kleppe and Rosa M. Miró-Roig
Journal: Proc. Amer. Math. Soc. 139 (2011), 3831-3843
MSC (2010): Primary 14M12, 14C05, 14H10, 14J10
DOI: https://doi.org/10.1090/S0002-9939-2011-10802-5
Published electronically: March 16, 2011
MathSciNet review: 2823030
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Abstract: Given integers $a_0\le a_1\le \cdots \le a_{t+c-2}$ and $b_1\le \cdots \le b_t$, we denote by $W(\underline {b};\underline {a})\subset \textrm {Hilb}^p(\mathbb {P}^{n})$ the locus of good determinantal schemes $X\subset \mathbb {P}^{n}$ of codimension $c$ defined by the maximal minors of a $t\times (t+c-1)$ homogeneous matrix with entries homogeneous polynomials of degree $a_j-b_i$. The goal of this paper is to extend and complete the results given by the authors in an earlier paper and determine under weakened numerical assumptions the dimension of $W(\underline {b};\underline {a})$ as well as whether the closure of $W(\underline {b};\underline {a})$ is a generically smooth irreducible component of $\textrm {Hilb}^p(\mathbb {P}^{n})$.


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Additional Information

Jan O. Kleppe
Affiliation: Faculty of Engineering, Oslo University College, Pb. 4 St. Olavs plass, N-0130 Oslo, Norway
Email: JanOddvar.Kleppe@iu.hio.no

Rosa M. Miró-Roig
Affiliation: Departament d’Algebra i Geometria, Facultat de Matemàtiques, Universitat Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain
MR Author ID: 125375
ORCID: 0000-0003-1375-6547
Email: miro@ub.edu

Received by editor(s): November 10, 2009
Received by editor(s) in revised form: September 17, 2010
Published electronically: March 16, 2011
Additional Notes: The second author was partially supported by MTM2010-15256.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2011 American Mathematical Society