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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Linear series with cusps and $ n$-fold points


Author: David Schubert
Journal: Trans. Amer. Math. Soc. 304 (1987), 689-703
MSC: Primary 14H10; Secondary 14C20
DOI: https://doi.org/10.1090/S0002-9947-1987-0911090-X
MathSciNet review: 911090
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Abstract: A linear series $ (V,\,\mathcal{L})$ on a curve $ X$ has an $ n$-fold point along a divisor $ D$ of degree $ n$ if $ \dim (V \cap {H^0}(X,\,\mathcal{L}( - D))) \geqslant \dim (V) - 1$. The linear series has a cusp of order $ e$ at a point $ P$ if $ \dim (V \cap {H^0}(X,\,\mathcal{L}( - (e + 1)P))) \geqslant \dim (V) - 1$. Linear series with cusps and $ n$-fold points are shown to exist if certain inequalities are satisfied. The dimensions of the families of linear series with cusps are determined for general curves.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0911090-X
Article copyright: © Copyright 1987 American Mathematical Society