Communications in Algebra | 2019
On the existence of superspecial and maximal nonhyperelliptic curves of genera four and five
Abstract
Abstract This article shows the existence of superspecial and maximal nonhyperelliptic curves of genera four and five in characteristic p\u2009>\u20090 for infinitely many primes p. Specifically, we prove that the variety in the projective three-space with p\u2009>\u20092 is a maximal superspecial nonhyperelliptic curve of genus four if and only if We also prove that the desingularization Tp of is a maximal superspecial trigonal curve of genus five if and only if or Moreover, we give families of maximal curves of more general type, which include Tp.