Linear series with an 𝑁-fold point on a general curve

Schubert, David

doi:10.1090/S0002-9947-1991-1005937-X

Linear series with an $N$-fold point on a general curve
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Trans. Amer. Math. Soc. 327 (1991), 117-124 Request permission

Abstract:

A linear series $(V,\mathcal {L})$ on a curve $X$ has an $N$-fold point along a divisor $D$ of degree $N$ if $\dim (V \cap {H^0}\;(X,\mathcal {L} (- D))) \geq \dim \;V - 1$. The dimensions of the families of linear series with an $N$-fold point are determined for general curves.

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