IJPAM: Volume 98, No. 3 (2015)

ON WEIERTRASS $N$-SEMIGROUPS
ON SMOOTH CURVES

E. Ballico
Department of Mathematics
University of Trento
38 123 Povo (Trento) - Via Sommarive, 14, ITALY


Abstract. Let $X$ be a smooth curve of genus $g>0$. For any $n\ge 2$ and any $n$ distinct points $P_1,\dots ,P_n\in X$ let $E(P_1,\dots ,P_n)$ be the set of all $(a_1,\dots ,a_n)\in \mathbb {N}^n$ such that $\mathcal {O}_X(a_1P_1+\cdots +a_nP_n)$ is spanned. We study some abstract properties of the semigroup $E(P_1,\dots ,P_n)$ (e.g. its decompositions in irreducibles) which are upper bounded by a function of $g$ independent from $n$. We say that $E(P_1,\dots ,P_n)$ is symmetric if $\mathcal {O}_X(a_1P_1+\cdots +a_nP_n) \cong \omega _X$ for some $(a_1,\dots ,a_n)\in \mathbb {N}^n$. We study symmetric $n$-semigroups of curves with general moduli.

Received: August 24, 2014

AMS Subject Classification: 14N05

Key Words and Phrases: Weiertrass $n$-semigroup, smooth curve, semigroup of non-gaps

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DOI: 10.12732/ijpam.v98i3.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 98
Issue: 3
Pages: 333 - 338


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