论文标题
曲线对称产品的有效锥
Effective cone of the blow up of the symmetric product of a curve
论文作者
论文摘要
令$ c $为$ g \ geq 1 $的平滑曲线，让$ c^{（2）} $成为其第二个对称产品。在本说明中，我们证明，如果$ c $非常笼统，那么在非常通用的点上$ c^{（2）} $的爆炸具有非多层伪有效的锥体。该策略首先要考虑过椭圆形曲线的情况，然后表明具有多面体伪有效的锥体是表面家庭的封闭特性。
Let $C$ be a smooth curve of genus $g \geq 1$ and let $C^{(2)}$ be its second symmetric product. In this note we prove that if $C$ is very general, then the blow-up of $C^{(2)}$ at a very general point has non-polyhedral pseudo-effective cone. The strategy is to consider first the case of hyperelliptic curves and then to show that having polyhedral pseudo-effective cone is a closed property for families of surfaces.
