Some arithmetic properties of order-sequences of algebraic curves
Let \(L\) be the linear system of hyperplane sections on a smooth projective curve embedded in the projective \(N\)-space. For a divisor \(D\) on the curve \(X\), over an algebraically closed field, let \(e(D,P)\) denote the order of \(D\) at \(P\) on \(X\). One defines the order sequence at \(P\) for \(L\) as the \(N+1\) different orders at \(P\) as \(D\) runs through all the divisors in \(L\). The generic order sequence is called the order sequence of \(L\). The author gives a new proof of the inequalities of the order sequence of \(L\) that was shown by \textit{M. Homma} [``Linear systems on curves with no Weierstrass points'', Bol. Soc. Bras. Mat., Nova Ser. 23, No. 1-2, 93-108 (1992)]. In addition he gives equivalent conditions for when equalities hold and an inequality on order-sequences at Weierstrass points on canonical curves.
scientific article; zbMATH DE number 167300
scientific article