mini-symposium

"Wind from Rio, IV"

"Classes of curves with special Weierstrass points"

Eduardo de Sequeira Esteves (IMPA, Brazil)

ABSTRACT: Let M be the moduli space of stable curves of genus g. Let D be the closure in M of the locus of smooth curves possessing a point P such that (g-1)P moves in a pencil, and E the closure of the locus of smooth curves possessing a point P such that (g+1)P moves in a net. In the 80's Diaz computed the class of D in the Picard group of M, and later Cukierman used Diaz's result to compute the class of E. We will see how to compute the two classes in a unified way: at the same time through the same method. In the process, we will solve a few enumerative problems for two-pointed curves, and describe limits of special Weierstrass points. This is joint work with Letterio Gatto and Caterina Cumino.