用曲线上的移动分支枚举铅笔

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2019-07-22 DOI:10.1090/jag/776

Carl Lian

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引用次数: 8

摘要

考虑在可能移动的点上，在分支条件下，从一条固定的一般曲线上枚举投影线的分支覆盖的一般问题。我们主要计算属1;极限线性级数理论允许我们简化到这种情况。我们首先得到一个简单的公式，计算固定椭圆曲线E E上铅笔的加权计数，其中基准点是允许的。然后，我们使用包含-排除过程，推导出具有移动分支条件的映射E→P 1 E\到\mathbb {P}^1的数目公式。一个显著的结果是，这些计数在一定的对合下是不变的。我们的结果推广了Harris, Logan, Osserman和Farkas-Moschetti-Naranjo-Pirola的工作。

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Enumerating pencils with moving ramification on curves

We consider the general problem of enumerating branched covers of the projective line from a fixed general curve subject to ramification conditions at possibly moving points. Our main computations are in genus 1; the theory of limit linear series allows one to reduce to this case. We first obtain a simple formula for a weighted count of pencils on a fixed elliptic curve E E , where base-points are allowed. We then deduce, using an inclusion-exclusion procedure, formulas for the numbers of maps E → P 1 E\to \mathbb {P}^1 with moving ramification conditions. A striking consequence is the invariance of these counts under a certain involution. Our results generalize work of Harris, Logan, Osserman, and Farkas-Moschetti-Naranjo-Pirola.

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.