Work

A family of non-isomorphic maximal function fields

Year: 2024

Type: article

Abstract: The problem of understanding whether two given function fields are isomorphic is well-known to be difficult, particularly when the aim is to prove that an isomorphism does not exist. In this paper we investigate a family of maximal function fields that arise as Galois subfields of the Hermitian function field. We compute the automorphism group, the Weierstrass semigroup at some special rational places and the isomorphism classes of such function fields. In this way, we show that often these function fields provide in fact examples of maximal function fields with the same genus, the same automorphism group, but that are not isomorphic.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-024-03650-1

Authors: Peter Beelen, Maria Montanucci, Jonathan Niemann, Luciane Quoos

Institutions: Technical University of Denmark, Universidade Federal do Rio de Janeiro

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Villum Fonden, Danmarks Tekniske Universitet