16 research outputs found
A note on the multiplicity of determinantal ideals
Herzog, Huneke, and Srinivasan have conjectured that for any homogeneous
-algebra, the multiplicity is bounded above by a function of the maximal
degrees of the syzygies and below by a function of the minimal degrees of the
syzygies. The goal of this paper is to establish the multiplicity conjecture of
Herzog, Huneke, and Srinivasan about the multiplicity of graded Cohen-Macaulay
algebras over a field for -algebras being a
determinantal ideal of arbitrary codimension
Ideals generated by submaximal minors
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 with entries homogeneous forms of degree a_j-b_i. Under
some numerical assumption on a_j and b_i we prove that the closure of W(b;a) is
an irreducible component of Hilb^{p(x)}(P^n), we show that Hilb^{p(x)}(P^n) is
generically smooth along W(b;a) and we compute the dimension of W(b;a) in terms
of a_j and b_i. To achieve these results we first prove that X is determined by
a regular section of the twisted conormal sheaf I_Y/I^2_Y(s) where
s=deg(det(A)) and Y is a codimension 2, arithmetically Cohen-Macaulay scheme of
P^n defined by the maximal minors of the matrix obtained deleting a suitable
row of A.Comment: 22 page
On the normal sheaf of determinantal varieties
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 \shN_X. We prove that under some mild restrictions: (1) there exists a line bundle \shL on X-Sing(X) such that \shN_X \otimes \shL is arithmetically Cohen–Macaulay and, even more, it is Ulrich whenever the entries of A are linear forms, (2) \shN_X is simple (hence, indecomposable) and, finally, (3) \shN_X is \mu-(semi)stable provided the entries of A are linear form
On the Weak Lefschetz Property for Artinian Gorenstein algebras of codimension three
We study the problem of whether an arbitrary codimension three graded
artinian Gorenstein algebra has the Weak Lefschetz Property. We reduce this
problem to checking whether it holds for all compressed Gorenstein algebras of
odd socle degree. In the first open case, namely Hilbert function
(1,3,6,6,3,1), we give a complete answer in every characteristic by translating
the problem to one of studying geometric aspects of certain morphisms from
to , and Hesse configurations in .Comment: A few changes with respect to the previous version. 17 pages. To
appear in the J. of Algebr
Bounds for the Betti numbers of generalized Cohen-Macaulay ideals
Upper bounds for the Betti numbers of generalized Cohen-Macaulay ideals are given. In particular, for the case of non-degenerate, reduced and ir- reducible projective curves we get an upper bound which only depends on their degree