Limit Weierstrass points on nodal reducible curves |
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Authors: | Eduardo Esteves Parham Salehyan |
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Affiliation: | Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110, 22460-320 Rio de Janeiro RJ, Brazil ; Departament of Mathematics, IBILCE, Universidade Estadual Paulista (UNESP), Rua Cristóvão Colombo, 2265, 15054-000 São José do Rio Preto SP, Brazil |
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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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