论文标题
小型第二个Chern类和Mestrano-Simpson猜想的一般六束表面上的一些束束的几何形状
Geometry of some moduli of bundles over a very general sextic surface for small second Chern classes and Mestrano-Simpson Conjecture
论文作者
论文摘要
令$ s \ subset \ mathbb p^3 $在复数上是非常通用的六曲表面。令$ \ MATHCAL {M}（H，C_2）$是$ 2 $稳定捆绑$ s $的模量空间，带有固定的首先Chern类$ H $和第二Chern Class $ C_2 $。在本文中，我们研究了满足Cayley-Bacharach属性的某些降低零尺寸尺寸的点的配置，这导致了Moduli Space的一般模仿空间的一般成员的非平凡部分，用于小$ C_2 $。使用这项研究，我们将试图证明Mestrano-simpson的猜想对$ \ Mathcal {M} {M}（H，11）$的不可约组件的数量，并部分证明了猜想。我们还将证明$ \ MATHCAL {M}（H，C_2）$对于$ C_2 \ le 10 $不可记述。
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 $c_2 \le 10$ .
