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Transactions of the American Mathematical Society

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

 
 

 

Generalised Castelnuovo inequalities


Author: Liam A. Donohoe
Journal: Trans. Amer. Math. Soc. 344 (1994), 217-260
MSC: Primary 14H10; Secondary 14H45
DOI: https://doi.org/10.1090/S0002-9947-1994-1208880-9
MathSciNet review: 1208880
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Abstract: Given a Riemann surface of genus p, denoted by ${X_p}$, admitting j linear series of dimension r and degree n Accola derived a polynomial function $f(j,n,r)$ so that $p \leq f(j,n,r)$ and exhibited plane models of Riemann surfaces attaining equality in the inequality. In this paper we provide a classification of all such ${X_p}$ when $r \geq 6$. In addition we classify curves, ${X_p}$, of maximal genus when ${X_p}$ admits two linear series which have a common dimension but different degrees.


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Article copyright: © Copyright 1994 American Mathematical Society