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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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