论文标题
关于任意特征的versei问题
On the Severi problem in arbitrary characteristic
论文作者
论文摘要
在本文中，我们表明，在任何特征中，severi品种参数化了给定程度和几何属的不可还原的平面曲线和几何属。遵循Severi的最初想法，这给出了一个新的证明，证明了在积极特征中给定属的平滑投射曲线的模量空间的不可约性。这是第一个证明，涉及特征性零案例不减少。进一步的结果，我们将Zariski的定理推广到阳性特征，并表明给定几何属的一般平面曲线是节点。
In this paper, we show that Severi varieties parameterizing irreducible reduced planar curves of a given degree and geometric genus are either empty or irreducible in any characteristic. Following Severi's original idea, this gives a new proof of the irreducibility of the moduli space of smooth projective curves of a given genus in positive characteristic. It is the first proof that involves no reduction to the characteristic zero case. As a further consequence, we generalize Zariski's theorem to positive characteristic and show that a general reduced planar curve of a given geometric genus is nodal.
