Geometry of curves with exceptional secant planes
Geometry of curves with exceptional secant planes
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发表时间：
2007-06
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通讯作者：
Ethan Cotterill
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作者：
Ethan Cotterill
我们研究的曲线与线性系列是例外的关于他们的割线平面。工作的Brill-Noether理论对线性级数的扩展的框架中，我们证明了一般曲线的属g没有例外的割线平面，在一个非常精确的意义。我们还解决了计算问题的线性级数与例外割线平面在一个单参数家庭的重言式类与家庭。我们得到了与级数g^{2d-1}_m$相关的允许d$-割线$（d-2）$-平面的割线平面公式重言式系数的生成函数。我们还描述了一种策略，用于计算类的因子相关的例外割线平面行为的Picard群的曲线的模空间中的一对夫妇的自然产生的无限家庭的情况下，我们给出了一个公式的数目与例外割线平面上的一般曲线配备了一个一维家庭的线性级数。
We study curves with linear series that 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 of genus g has no exceptional secant planes, in a very precise sense. We also address 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. We obtain conjectural generating functions for the tautological coefficients of secant-plane formulas associated to series $g^{2d-1}_m$ that admit $d$-secant $(d-2)$-planes. We also describe a strategy for computing the classes of divisors associated to exceptional secant plane behavior in the Picard group of the moduli space of curves in a couple of naturally-arising infinite families of cases, and we give a formula for the number of linear series with exceptional secant planes on a general curve equipped with a one-dimensional family of linear series.