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Now showing items 1-10 of 14

#### Components of the Hilbert scheme of space curves on low-degree smooth surfaces

(World Scientific Publishing, 2015-02-27)

We study maximal families W of the Hilbert scheme, H(d, g)sc, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth ...

#### Families of artinian and low dimensional determinantal rings.

(Elsevier, 2017)

Let GradAlg(H) be the scheme parameterizing graded quotients of R = k[x_0,...,x_n] with Hilbert function
H (it is a subscheme of the Hilbert scheme of P^n if
we restrict to quotients of positive dimension, see ...

#### Deformations of modules of maximal grade and the Hilbert scheme at determinantal schemes

(Elsevier, 2014-04-04)

Let R be a polynomial ring and M a finitely generated graded R-module of maximal grade (which means that the ideal I_t(\cA) generated by the maximal minors of a homogeneous presentation matrix, \cA, of M has maximal ...

#### On the normal sheaf of determinantal varieties

(De Gruyter, 2014-06-18)

Let X be a standard determinantal scheme X of P^n of codimension c, i.e. a scheme defined by the maximal minors of a tx(t+c-1)homogeneous polynomial matrix A. In this paper, we study the main features of its normal sheaf ...

#### The Hilbert Scheme of Buchsbaum space curves

(Association des Annales de l'Institute Fourier, 2012)

We consider the Hilbert scheme H(d,g) of space curves C with homogeneous ideal I(C):=H_{*}^0(\sI_C) and Rao module M:=H_{*}^1(\sI_C). By taking suitable generizations (deformations to a more general curve C') of C, we ...

#### Families of Determinantal Schemes

(American Mathematical Society, 2011-03-16)

Given integers a_0 <= a_1 <= ... <= a_{t+c-2} and b_1 <= ... <= b_t, we denote by W(b;a) \subset Hilb^p(P^n) the locus of good determinantal schemes X in P^n of codimension c defined by the maximal minors of a t x (t+c-1) ...

#### The Hilbert scheme of space curves sitting on a smooth surface containing a line

(Springer Verlag, 2016-10-14)

We continue the study of maximal families W of the Hilbert
scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth degree-s surface S containing a line. For s > 3, we extend the two ...

#### Families of low dimensional determinantal schemes

(Elsevier, 2010-11-09)

A scheme X in P^n of codimension c is called standard determinantal if its homogeneous saturated ideal can be generated by the t x t minors of a homogeneous t x (t+c-1) matrix (f_{ij}). Given integers a_0 <= a_1 <= ... <= ...

#### Ideals generated by submaximal minors

(Mathematical Science Publishers, 2009)

The goal of this paper is to study irreducible families W(b;a) of codimension 4, arithmetically Gorenstein schemes X of P^n defined by the submaximal minors of a t x t matrix A whose entries are homogeneous forms of degree ...

#### Unobstructedness and dimension of families of Gorenstein algebras

(Universitat de Barcelona, 2007)

The goal of this paper is to develop tools to study maximal families of Gorenstein quotients A of a polynomial ring R. We prove a very general Theorem on deformations of the homogeneous coordinate ring of a scheme Proj A ...