Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
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

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

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