论文标题
紧凑型曲线的连贯系统
Coherent systems on curves of compact type
论文作者
论文摘要
令$ c $成为紧凑型类型的两极分化节点曲线。在本文中，我们在$ c $上研究连贯的系统$（e，v）$，由深度为$ c $的每个不可约组件和一个子空间$ v \ subset h^0（e）$ k $。 King和Newstead引入了稳定相干系统的模量空间，并取决于真实的参数$α$。我们表明，当$ k \ geq r $时，这些模量空间以$α$足够大。然后，我们处理案例$ k = r+1 $：当$ e $的限制程度足够大时，我们可以使用双跨度构造来描述该模量空间的不可约组件。
Let $C$ be a polarized nodal curve of compact type. In this paper we study coherent systems $(E,V)$ on $C$ given by a depth one sheaf $E$ having rank $r$ on each irreducible component of $C$ and a subspace $V \subset H^0(E)$ of dimension $k$. Moduli spaces of stable coherent systems have been introduced by King and Newstead and depend on a real parameter $α$. We show that when $k \geq r$, these moduli spaces coincide for $α$ big enough. Then we deal with the case $k=r+1$: when the degrees of the restrictions of $E$ are big enough we are able to describe an irreducible component of this moduli space by using the dual span construction.
