论文标题
尺寸极化表面上的矢量场
Vector fields on canonically polarized surfaces
论文作者
论文摘要
本文研究了在具有非平凡的全局矢量场的积极特征领域定义的规范两极化表面的几何形状，以及这种表面存在在规范极化表面的模量问题中的含义。特别是，使用以下属性获得了显式整数值f（x）。如果x是一个规范极化的表面，其特征性p> 0的代数闭合场定义了典型的奇异性，使得p> f（k_x^2）和x具有非平凡的全球矢量场，则x是URIRATICATION，并且代数基本组是微不足道的。由于这一结果，确定了大量的规范两极化的表面，其模量堆栈是Deligne-Mumford，这是一种通常不具有正面特征的属性。 本文在数学上与以前的版本相同。替换论文的原因是为了指出，本文是对奇异表面的概括，其典型的奇异性是“矢量场和阳性特征的规范极化表面”的概括：1710.03076仅处理了平滑表面的情况。本文的结果将上述纸张的结果取代了其过时。
This paper investigates the geometry of canonically polarized surfaces defined over a field of positive characteristic which have a nontrivial global vector field, and the implications that the existence of such surfaces has in the moduli problem of canonically polarized surfaces. In particular, an explicit integer valued function f(x) is obtained with the following properties. If X is a canonically polarized surface with canonical singularities defined over an algebraically closed field of characteristic p>0 such that p>f(K_X^2) and X has a nontrivial global vector field, then X is unirational and the algebraic fundamental group is trivial. As a consequence of this result, large classes of canonically polarized surfaces are identified whose moduli stack is Deligne-Mumford, a property that does not hold in general in positive characteristic. This paper is mathematically identical to the previous version. The reason that the paper is replaced is in order to point out that this paper is a generalization to the case of singular surfaces with canonical singularities of the paper "Vector fields and moduli of canonically polarized surfaces in positive characteristic" with reference arXiv:1710.03076 which treated only the case of smooth surfaces. The results of this paper supercede the results of the aforementioned paper making it obsolete.
