论文标题
在光滑的投影曲线上的一些引号方案的NEF锥
Nef cones of some Quot schemes on a smooth projective curve
论文作者
论文摘要
让$ c $成为$ \ mathbb c $的光滑投射曲线。令$ n，d \ geq 1 $。令$ \ Mathcal Q $是矢量束的参数化扭转商$ \ Mathcal o^n_c $ $ d $。在本文中，我们研究了$ \ Mathcal Q $的Nef锥。在椭圆曲线的情况下，我们对NEF锥的完整描述。在$ d = 2 $和$ c $的情况下，我们将其计算为$ c $的第二个对称产品的Nef锥。如果$ n \ geq d $和$ c $非常通用时，我们为NEF圆锥提供了上限和下限。通常，我们为$ \ Mathcal Q $的除数提供了必要和足够的标准。
Let $C$ be a smooth projective curve over $\mathbb C$. Let $n,d\geq 1$. Let $\mathcal Q$ be the Quot scheme parameterizing torsion quotients of the vector bundle $\mathcal O^n_C$ of degree $d$. In this article we study the nef cone of $\mathcal Q$. We give a complete description of the nef cone in the case of elliptic curves. We compute it in the case when $d=2$ and $C$ very general, in terms of the nef cone of the second symmetric product of $C$. In the case when $n\geq d$ and $C$ very general, we give upper and lower bounds for the Nef cone. In general, we give a necessary and sufficient criterion for a divisor on $\mathcal Q$ to be nef.
