论文标题
关于Hilbert的模量空间的Hilbert方案
On the Hilbert scheme of the moduli space of torsion free sheaves on surfaces
论文作者
论文摘要
本文的目的是确定在表面上无扭转的束带的Moduli空间的Hilbert方案的不可还原成分的尺寸的结合。令$ x $为非单明性不可约合的复杂表面，让$ e $为$ x $上的等级$ n $的矢量捆绑包。我们在x $中使用$ e $的$ m $ - 元素转换，以表明存在格拉斯曼尼亚品种$ \ mathbb {g}（e_x，m）$中的嵌入到无扭转空间中的托架空间中注射式形态从$ x \ times m_ {x，h}（n; c_1，c_2）$到$ hilb _ {\，\ Mathfrak {\ Mathfrak {m} _ {x，h}（x，h}（n; c_1，c_1，c_2+m）} $。
The aim of this paper is to determine a bound of the dimension of an irreducible component of the Hilbert scheme of the moduli space of torsion-free sheaves on surfaces. Let $X$ be a non-singular irreducible complex surface and let $E$ be a vector bundle of rank $n$ on $X$. We use the $m$-elementary transformation of $E$ at a point $x \in X$ to show that there exists an embedding from the Grassmannian variety $\mathbb{G}(E_x,m)$ into the moduli space of torsion-free sheaves $\mathfrak{M}_{X,H}(n;c_1,c_2+m)$ which induces an injective morphism from $X \times M_{X,H}(n;c_1,c_2)$ to $Hilb_{\, \mathfrak{M}_{X,H}(n;c_1,c_2+m)}$.
