类属上割线约数的高阶分支与变种 曲线

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摘要翻译：
对于光滑射影曲线，e正割k平面的圈是经典枚举几何中研究最多的对象之一，并有Castelnuovo、Cayley和MacDonald关于它们的著名公式。尽管进行了各种尝试，但令人惊讶的是，对这些公式的枚举有效性知之甚少。本文的目的是在给定亏格的一般曲线C的情况下彻底澄清这个问题。利用退化技术和稳定点曲线模空间双形几何的一些事实，精确地确定了非空E正割K平面在何种条件下的圈，并计算了它的维数。我们还精确地确定了C带E割线K-平面上线性级数的维数。在另一个方向上，在本文的最后一部分，我们研究了C上线丛的幂在给定点有规定分支的分支点的分布。
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英文标题：
《Higher ramification and varieties of secant divisors on the generic
  curve》
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作者：
Gavril Farkas
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最新提交年份：
2014
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  For a smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to completely clarify this problem in the case of the generic curve C of given genus. Using degeneration techniques and a few facts about the birational geometry of moduli spaces of stable pointed curves we determine precisely under which conditions the cycle of e-secant k-planes in non-empty and we compute its dimension. We also precisely determine the dimension of the variety of linear series on C carrying e-secant k-planes. In a different direction, in the last part of the paper we study the distribution of ramification points of the powers of a line bundle on C having prescribed ramification at a given point.
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PDF链接：
https://arxiv.org/pdf/0704.0874

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关键词：distribution mathematics surprising prescribed Projective 给定 generic 平面 正割 研究