Resumen de Higher ramification and varieties of secant divisors on the generic curve

Gavril Farkas

• For a smooth projective curve, the cycles of e-secant k-planes are among the most studied objects in classical enumerative geometry, and there are well-known formulas due to Castelnuovo, Cayley and MacDonald concerning them. Despite various attempts, surprisingly little is known about the enumerative validity of such formulas. The aim of this paper is to clarify this problem in the case of the generic curve C of given genus. We determine precisely under which conditions the cycle of e-secant k-planes is non-empty, and we compute its dimension. We also precisely determine the dimension of the variety of linear series on C carrying e-secant k-planes