论文标题
曲线在某些偏光曲面上的变性
Degeneration of curves on some polarized toric surfaces
论文作者
论文摘要
我们解决了以下问题：给定极化的感谢您的表面（s，l）和线性系统中几何属G的一般积分曲线c | l |，是否存在| l |中的C退化。对于较小的几何属的一般积分曲线？我们对与H-透明多边形相关的表面的这个问题给出了肯定的答案，但前提是地面的特征足够大。我们给出了小特征表面的示例，对问题的答案是负面的。如果答案是肯定的，我们推断出上述一般曲线C是节点。在特征0中，我们使用结果表明具有H-透明多边形的大型偏光曲面表面的Severi品种的不可约性。
We address the following question: Given a polarized toric surface (S,L), and a general integral curve C of geometric genus g in the linear system |L|, do there exist degenerations of C in |L| to general integral curves of smaller geometric genera? We give an affirmative answer to this question for surfaces associated to h-transverse polygons, provided that the characteristic of the ground field is large enough. We give examples of surfaces in small characteristic, for which the answer to the question is negative. In case the answer is affirmative, we deduce that a general curve C as above is nodal. In characteristic 0, we use the result to show irreducibility of Severi varieties of a large class of polarized toric surfaces with h-transverse polygon.
