Mara Ungureanu

For a smooth projective curve, the varieties parametrising its secant planes are among the most studied objects in classical enumerative geometry.  We shall begin by reviewing some of their well-known properties, by formulating the problem in terms of secant divisors to a given linear series on the curve.  We consider in particular the enumerative formulas counting the number of divisors in the intersection of two such secant varieties corresponding to two distinct linear series on the curve and discuss their validity in terms of transversality of intersection of subvarieties inside the symmetric product of the curve.