For a smooth projective curve, the cycles of subordinate or, more generally, secant divisors to a given linear series are among some of the most studied objects in classical enumerative geometry. We consider the intersection of two such cycles corresponding to secant divisors of two different linear series on the same curve and investigate the validity of the enumerative formulae counting the number of divisors in the intersection. We study some interesting cases, with unexpected transversality properties, and establish a general method to verify when this intersection is empty.

中文翻译：

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一些割线变种与代数曲线的交点的几何

对于平滑的投影曲线，给定线性序列的从属或更广义的割除数的周期属于古典枚举几何中研究最多的对象之一。我们考虑对应于同一条曲线上两个不同线性序列的割线除数的两个这样的循环的交点，并研究计算相交数的枚举公式的有效性。我们研究了一些有趣的情况，这些情况具有出乎意料的横向性质，并建立了一种通用方法来验证此交集何时为空。