The space of nodal curves of type p,q with given Weierstra\ss semigroup
Helmut Knebl (1), Ernst Kunz (2), Rolf Waldi (2) ((1) Fakult\"at, Informatik, Georg-Simon-Ohm-Hochschule N\"urnberg, Germany, (2) Fakult\"at, f\"ur Mathematik, Universit\"at Regensburg, Germany)
TL;DR
This paper explores the structure of nodal curves of type p,q with specified Weierstraß semigroups, providing new criteria and identifying previously uncharacterized semigroups.
Contribution
It offers a necessary and sufficient criterion for a numerical semigroup to be a Weierstraß semigroup and introduces a new class of such semigroups.
Findings
Established a criterion for Weierstraß semigroups
Identified a new class of Weierstraß semigroups
Analyzed the space of nodal curves with given semigroup
Abstract
We continue the investigation of curves of type p,q started in [KKW]. We study the space of such curves and the space of nodal curves with prescribed Weierstra\ss semigroup. A necessary and sufficient criterion for a numerical semigroup to be a Weierstra\ss semigroup is given. We find a class of Weierstra\ss semigroups which apparently has not yet been described in the literature.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory