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International Mathematics Research Papers (2008) Vol. 2008 : article ID rpn001, 65 pages, doi:10.1093/imrp/rpn001 published on April 1, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Limits of Special Weierstrass Points

C. Cumino1, E. Esteves2 and L. Gatto1

1 Dipartimento di Matematica, Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino, Italy
2 Instituto Nacional de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil

Correspondence: Correspondence to be sent to: IMPA, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brazil. e-mail: esteves{at}impa.br

Let C be the union of two general connected, smooth, nonrational curves X and Y intersecting transversally at a point P. Assume that P is a general point of X or of Y. Our main result describes all limits on C of special Weierstrass points along smooth curves degenerating to C. As an application, we recover in a unified and conceptually simpler way the computations made by Diaz and Cukierman of divisor classes of curves with special Weierstrass points in the moduli space of stable curves. In our approach there are no multiplicity issues, an usual nuisance of the method of test curves.


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