Some families of non-isomorphic maximal function fields
arxiv(2024)
摘要
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.
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