ALGA - 2001

Fourth Meeting of the Brazilian Group in

Commutative Algebra and Algebraic Geometry

Hotel Portogalo, Angra dos Reis, August 5-11, 2001

Degeneration of special Weierstrass points on stable curves

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Abstract

I will report on a joint work with C. Cumino (Politecnico di Torino). Let C₀ be a stable projective complex curve of genus g. One says that a point P is limit of a special Weierstrass point on nearby smooth curves if there exists a one parameter family (X_t,P_t) of stable pointed curves in a neighbourhood of t=0, such that X_t is smooth, P_t is a special Weierstrass point for t≠0 and P₀=P. Suppose that C₀ is a general uninodal stable curve. We offer a characterization of the points which are limit of special Weierstrass points on nearby smooth curves on C₀, showing enumerative applications to the computations of certain divisor classes in the Picard Group of the Moduli Functor of stable curves of genus g.

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poster by Renata Maiato

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