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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: April 16, 2007
MathSciNet review: 2320659
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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: http://dx.doi.org/10.1090/S0002-9947-07-04193-1
PII: S 0002-9947(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