Limit Weierstrass points on nodal reducible curves

Authors:
Eduardo Esteves and Parham Salehyan

Journal:
Trans. Amer. Math. Soc. **359** (2007), 5035-5056

MSC (2000):
Primary 14H10, 14H55

DOI:
https://doi.org/10.1090/S0002-9947-07-04193-1

Published electronically:
April 16, 2007

MathSciNet review:
2320659

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Abstract | References | Similar Articles | Additional Information

Abstract: In the 1980s D. Eisenbud and J. Harris posed the following question: ``What are the limits of Weierstrass points in families of curves degenerating to stable curves *not* of compact type?'' In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

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Additional Information

**Eduardo Esteves**

Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro RJ, Brazil

Email:
esteves@impa.br

**Parham Salehyan**

Affiliation:
Departament of Mathematics, IBILCE, Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto SP, Brazil

Email:
parham@ibilce.unesp.br

DOI:
https://doi.org/10.1090/S0002-9947-07-04193-1

Received by editor(s):
April 4, 2005

Received by editor(s) in revised form:
September 19, 2005

Published electronically:
April 16, 2007

Additional Notes:
The first author was supported by CNPq, Proc. 300004/95-8

The second author was supported by CNPq, Proc. 142643/98-0 and 150258/03-8

Article copyright:
© Copyright 2007
American Mathematical Society