摘要翻译：
我们研究了G$属的一般曲线上的线性级数，它的象关于它们的割线平面是例外的。在将Brill-Noether理论推广到线性级数对的框架下，我们在非常精确的意义上证明了当级数总数有限时，一般曲线不存在具有例外割线平面的线性级数。其次，我们通过对我们的假设公式进行合理选择的检验族的评估，部分地解决了用与单参数族相关的重言类计算单参数族中具有例外割线平面的线性级数个数的问题。作为应用，我们计算了具有一维线性级数族的一般曲线上具有例外割线平面的线性级数的个数。在曲面上点的Hilbert格式的研究中，我们特别注意了$d$-割线$(d-2)$-平面到$(2d-1)$-维级数的极值情形。在这种情况下，我们的公式可以用超几何级数重写，这使得我们既可以证明它是非零的，又可以用$d$推导它的渐近性。
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英文标题：
《Geometry of curves with exceptional secant planes: linear series along
  the general curve》
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作者：
Ethan Cotterill
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最新提交年份：
2010
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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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一级分类：Mathematics        数学
二级分类：Combinatorics        组合学
分类描述：Discrete mathematics, graph theory, enumeration, combinatorial optimization, Ramsey theory, combinatorial game theory
离散数学，图论，计数，组合优化，拉姆齐理论，组合对策论
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英文摘要：
  We study linear series on a general curve of genus $g$, whose images are exceptional with regard to their secant planes. Working in the framework of an extension of Brill-Noether theory to pairs of linear series, we prove that a general curve has no linear series with exceptional secant planes, in a very precise sense, whenever the total number of series is finite. Next, we partially solve the problem of computing the number of linear series with exceptional secant planes in a one-parameter family in terms of tautological classes associated with the family, by evaluating our hypothetical formula along judiciously-chosen test families. As an application, we compute the number of linear series with exceptional secant planes on a general curve equipped with a one-dimensional family of linear series. We pay special attention to the extremal case of $d$-secant $(d-2)$-planes to $(2d-1)$-dimensional series, which appears in the study of Hilbert schemes of points on surfaces. In that case, our formula may be rewritten in terms of hypergeometric series, which allows us both to prove that it is nonzero and to deduce its asymptotics in $d$.
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PDF链接：
https://arxiv.org/pdf/0706.2049