403 research outputs found
Uniform Steiner bundles
In this work we study -type uniform Steiner bundles, being the lowest
degree of the splitting. We prove sharp upper and lower bounds for the rank in
the case and moreover we give families of examples for every allowed
possible rank and explain which relation exists between the families. After
dealing with the case in general, we conjecture that every -type uniform
Steiner bundle is obtained through the proposed construction technique.Comment: 23 pages, to appear at Annales de l'Institut Fourie
Families of determinantal schemes
Given integers a_0 \le a_1 \le ... \le a_{t+c-2} and b_1 \le ... \le b_t, we
denote by W(b;a) \subset Hilb^p(\PP^{n}) the locus of good determinantal
schemes X \subset \PP^{n} of codimension c defined by the maximal minors of a t
x (t+c-1) homogeneous matrix with entries homogeneous polynomials of degree
a_j-b_i. The goal of this short note is to extend and complete the results
given by the authors in [10] and determine under weakened numerical assumptions
the dimension of W(b;a), as well as whether the closure of W(b;a) is a
generically smooth irreducible component of the Hilbert scheme Hilb^p(\PP^{n}).Comment: The non-emptiness of W(b;a) is restated as (2.2) in this version; the
codimension c=2 case in (2.5)-(2.6) is reconsidered, and c > 2 (c > 3) is now
an assumption in (2.16)-(2.17). 13 page
Stability of syzygy bundles
We show that given integers , and such that ,
, and , there is a family of
monomials in of degree such that their syzygy
bundle is stable. Case was obtained independently by Coand\v{a} with
a different choice of families of monomials [Coa09].
For , there are monomials of degree~ in
such that their syzygy bundle is semistable.Comment: 16 pages, to appear in the Proceedings of the American Mathematical
Societ
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