WEIERSTRASS SEMIGROUPS AND AUTOMORPHISM GROUP OF A MAXIMAL CURVE WITH THE THIRD LARGEST GENUS

作     者：Beelen, Peter Montanucci, Maria Vicino, Lara 

作者机构：Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby2800 Denmark 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2023年

核心收录：

主　　题：Algebra 

摘      要：In this article we explicitly determine the Weierstrass semigroup at any point and the full automorphism group of a known Fq2-maximal curve χ3 having the third largest genus. This curve arises as a Galois subcover of the Hermitian curve, and its uniqueness (with respect to the value of its genus) is a well-known open problem. Knowing the Weierstrass semigroups may provide a key towards solving this problem. Surprisingly enough χ3 has many different types of Weierstrass semigroups and the set of its Weierstrass points is much richer than the set of Fq2-rational points, as instead happens for all the known maximal curves where the Weierstrass points are known. We show that a similar exceptional behaviour does not occur in terms of automorphisms, that is, Aut(χ3) is exactly the automorphism group inherited from the Hermitian curve, apart from small values of *** Codes Primary: 11G20. Secondary: 11R58, 14H05, 14H55 Copyright © 2023, The Authors. All rights reserved.