Geometry of some moduli of bundles over a very general sextic surface for small second Chern classes and Mestrano-Simpson Conjecture (original) (raw)
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arXiv: Algebraic Geometry, 2020
Let SsubsetmathbbP3S \subset \mathbb P^3SsubsetmathbbP3 be a very general sextic surface over complex numbers. Let mathcalM(H,c_2)\mathcal{M}(H, c_2)mathcalM(H,c2) be the moduli space of rank 222 stable bundles on SSS with fixed first Chern class HHH and second Chern class c2c_2c2. In this article we will classify the obstructed bundles in $ \mathcal{M}(H, c_2)$ for small c2c_2c2. Using this classification we will make an attempt to prove Mestrano-Simpson conjecture on the number of irreducible components of mathcalM(H,11)\mathcal{M}(H, 11)mathcalM(H,11) and prove the conjecture partially. We will also show that mathcalM(H,c2)\mathcal{M}(H, c_2)mathcalM(H,c_2) is irreducible for $c_2 \le 10
On moduli of stable 2-bundles with small chern classes onQ 3
Annali di Matematica Pura ed Applicata, 1994
Let M(Cl, c 2 ) be the moduli space of stable rank-2 vector bundles with Chern classes cl , c~. over the smooth quadric Qa c ~4. The main result of the paper consists in a description of M(O, 2) by studying the interplay between the quadrics determined by the jumping lines and the null-correlation over the spinor variety FS=Gr(F1, Qs). We describe also M(-1, 2), M( -1, 3) and M(O, 4). The irreducibility of M(O, 4) relies on the classification of cuwes Y c Q3 of degree 6 with wr = Oy(-1), achieved by Manolache in the appendix.
On Some Moduli Spaces of Bundles on K3 Surfaces
Monatshefte Fur Mathematik, 2005
We give infinitely many examples in which the moduli space of rank 2 H-stable sheaves on a K3 surface S endowed by a polarization H of degree 2g – 2, with Chern classes c 1 = H and c 2 = g – 1, is birationally equivalent to the Hilbert scheme S[g – 4] of zero dimensional subschemes of S of length g – 4. We get in this way a partial generalization of results from [5] and [1].
A Structure Theorem for SUC(2) and the Moduli of Pointed Genus Zero Curves
2009
Let SUC(2) be the moduli space of rank 2 semistable vector bundles with trivial determinant on a smooth complex curve C of genus g> 1,nonhyperellptic if g> 2. In this paper we prove a birational structure theorem for SUC(2) that generalizes that of [Bol07] for genus 2. Notably we give a description of SUC(2) as a fibration over P g, where the fibers are compactifications of the moduli space M0,2g of 2g-pointed genus zero curves. This is done by describing the classifying maps of extensions of the line bundles associated to some effective divisors. In particular, for g = 3 our construction shows that SUC(2) is birational to a fibration in Segre cubics over a P³.
New moduli components of rank 2 bundles on projective space
Sbornik: Mathematics, 2021
We present a new family of monads whose cohomology is a stable rank 2 vector bundle on . We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank 2 vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank 2 vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components. Bibliography: 40 titles.
A structure theorem for SU(2) and the moduli of pointed genus zero curves
2009
Let SU_C(2) be the moduli space of rank 2 semistable vector bundles with trivial de terminant on a smooth complex algebraic curve C of genus g > 1, we assume C non-hyperellptic if g > 2. In this paper we construct large families of pointed rational normal curves over certain linear sections of SU_C(2). This allows us to give an interpretation of these subvarieties of SUC(2) in terms of the moduli space of curves M_{0,2g}. In fact, there exists a natural linear map SU_C(2) -> P^g with modular meaning, whose fibers are birational to M_{0,2g}, the moduli space of 2g-pointed genus zero curves. If g < 4, these modular fibers are even isomorphic to the GIT compactification M^{GIT}_{0,2g}. The families of pointed rational normal curves are recovered as the fibers of the maps that classify extensions of line bundles associated to some effective divisors.