101 research outputs found
Non-obstructed subcanonical space curves
Recall that a closed subscheme X C P is non-obstructed if the corresponding point x of the Hilbert scheme Hilb'm is non-singular . A geometric characterization of non-obstructedness is not known even for smooth space curves . The goal of this work is to prove that subcanonical k-Buchsbaum, k _< 2, space curves are nonobstructed . As a main tool, we use Serre's correspondence between subcanonical curves and vector bundl
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
On the existence of generically smooth components for moduli spaces of rank 2 stable reflexive sheaves on P3
AbstractThe goal of this work is to prove that for almost all possible triples (c1, c2, c3) ϵ Z3 the moduli scheme M(2; c1, c2, c3), which parametrizes isomorphism classes of rank 2 stable reflexive sheaves on P3 with Chern classes c1, c2 and c3, has a generically smooth component. In order to obtain these results we construct a wide range of non-obstructed, m-normal curves with suitable degree and genus. We conclude this paper by adding some examples and remarks
Rank 2 stable vector bundles on Fano 3-folds of index 2
AbstractLet X be a Fano 3-fold of the first kind with index 2. In this paper, we characterize the chern classes of rank 2 stable vector bundles on X and we find a bound for the least twist of a rank 2 reflexive sheaf on X which has a global section
Dimension of families of determinantal schemes
A scheme of codimension is called standard determinantal if its homogeneous saturated ideal can be generated by the maximal minors of a homogeneous matrix and is said to be good determinantal if it is standard determinantal and a generic complete intersection. Given integers and we denote by (resp. ) the locus of good (resp. standard) determinantal schemes of codimension defined by the maximal minors of a matrix where is a homogeneous polynomial of degree .
In this paper we address the following three fundamental problems: To determine (1) the dimension of (resp. ) in terms of and , (2) whether the closure of is an irreducible component of , and (3) when is generically smooth along . Concerning question (1) we give an upper bound for the dimension of (resp. ) which works for all integers and , and we conjecture that this bound is sharp. The conjecture is proved for , and for under some restriction on and . For questions (2) and (3) we have an affirmative answer for and , and for under certain numerical assumptions
A lower bound for the number of components of the moduli schemes of stable rank 2 vector bundles on projective 3-folds
Fix a smooth projective 3-fold X, c1, H ∈ Pic(X) with H ample, and d ∈ Z. Assume the existence of integers a, b with a ≠ 0 such that ac1 is numerically equivalent to bH. Let M(X, 2, c1, d, H) be the moduli scheme of H-stable rank 2 vector bundles, E, on X with c1(E) = c1 and c2(E) · H = d. Let m(X, 2, c1, d, H) be the number of its irreducible components. Then lim supd→ ∞m(X, 2, c1, d, H) = +∞
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