Abstract
Given a Riemann surface of genus p, denoted by X p {X_p} , admitting j linear series of dimension r and degree n Accola derived a polynomial function f ( j , n , r ) f(j,n,r) so that p ≤ f ( j , n , r ) 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 {X_p} when r ≥ 6 r \geq 6 . In addition we classify curves, X p {X_p} , of maximal genus when X p {X_p} admits two linear series which have a common dimension but different degrees.
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