$$(3,\gamma )$-hyperelliptic 曲线的权重边界

Pub Date : 2024-02-05 DOI:10.1007/s10801-023-01295-7

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引用次数: 0

摘要

摘要 $(N,\gamma )$-((N,\gamma))半群是由 Fernando Torres 提出的，它概括了与（((N,\gamma))属曲线的 N 个折叠盖的完全横切点相关的 Weierstrass 半群的最显著性质。托雷斯描述了 $(2,\gamma )$-只要其属相对于 $\gamma ) 是大的，就具有最大权重的双曲半群。在这里，我们对（(3,\gamma )在这里，我们对 \((3,\gamma )$ -hyperelliptic semigroups 也做了同样的处理，并且我们对 $N \ge 3$ 是素数的一般情况提出了一个猜想。

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Weight bounds for $$(3,\gamma )$$ -hyperelliptic curves

Abstract

$(N,\gamma )$ -hyperelliptic semigroups were introduced by Fernando Torres to encapsulate the most salient properties of Weierstrass semigroups associated with totally ramified points of N-fold covers of curves of genus $\gamma $ . Torres characterized $(2,\gamma )$ -hyperelliptic semigroups of maximal weight whenever their genus is large relative to $\gamma $ . Here we do the same for $(3,\gamma )$ -hyperelliptic semigroups, and we formulate a conjecture about the general case whenever $N \ge 3$ is prime.

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