Geometry of intersections of some secant varieties to algebraic curves
Mathematisch-Naturwissenschaftliche Fakultät
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.
