The article “A family of non-isomorphic maximal function fields” by the algebra group members Peter Beelen, Maria Montanucci and Jonathan Tilling Niemann together with Luciane Quoos from the Federal University of Rio de Janeiro in Brazil has been accepted for publication in Mathematische Zeitschrift.
The paper deals with the problem of understanding whether two given function fields are isomorphic (well-known to be difficult), particularly when the aim is to prove that an isomorphism does not exist. In the article 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.
The paper was initiated when Luciane visited the algebra group in connection with the Ph.D. defence of Lara Vicino last January. For more info, take a look here.