Geometry of some moduli of bundles over a very general sextic surface for small second Chern classes and Mestrano-Simpson Conjecture

Abstract

Let $S\subset {\mathbb{P}}^3$ be a very general sextic surface over complex numbers. Let $\mathcal{M}(H,c_2)$ be the moduli space of rank $2$ stable bundles on $S$ with fixed first Chern class $H$ and second Chern class $c_2$. In this article we study the configuration of points of certain reduced zero dimensional subschemes on $S$ satisfying Cayley-Bacharach property, which leads to the existence of non-trivial sections of a general memeber of the moduli space for small $c_2$. Using this study we will make an attempt to prove Mestrano-Simpson conjecture on the number of irreducible components of $\mathcal{M}(H,11)$ and prove the conjecture partially. We will also show that $\mathcal{M}(H,c_2)$ is irreducible for $c_2\le 10$ .

Final version, to appear in Bull. Sci. Math

References in corpus (3)

• Irreducibility of the moduli space of stable vector bundles of rank two and odd degree on a very general quintic surface
• Seminatural bundles of rank two, degree one and $c_2=10$ on a quintic surface
• Non-emptiness of Brill-Noether Loci over very general quintic hypersurface