论文标题
$ \ mathbb {p}^2 $的一般爆破上的滑轮的模量空间
Moduli Spaces of Sheaves on General Blow-ups of $\mathbb{P}^2$
论文作者
论文摘要
令$ x $为$ \ mathbb {p}^2 $沿$ m $一般点的爆炸，$ a = h- \ sum \ sum \ varepsilon_ie_i $是$ 0 <\ varepsilon_i \ ll1 $的通用极化。我们对满足弱的Brill-Noether属性的Chern字符进行分类，即$ M_A（{\ BF {V}}）$中的一般捆，坡度稳定或骨带有Chern parnem $ {\ bf {v}} $的坡度稳定吊带的Moduli空间。我们进一步为存在稳定的滑轮提供了必要和充分的条件。我们的策略是专门研究$ M $点的案例。
Let $X$ be the blow-up of $\mathbb{P}^2$ along $m$ general points, and $A=H-\sum \varepsilon_iE_i$ be a generic polarization with $0<\varepsilon_i\ll1$. We classify the Chern characters which satisfy the weak Brill-Noether property, i.e. a general sheaf in $M_A({\bf{v}})$, the moduli space of slope stable sheaves with Chern character ${\bf{v}}$, has at most one non-zero cohomology. We further give a necessary and sufficient condition for the existence of stable sheaves. Our strategy is to specialize to the case when the $m$ points are collinear.
