Automorphism groups of superspecial curves of genus $4$ over ${\mathbb{F}}_{11}$

Abstract

In this paper, we explicitly determine the automorphism group of every nonhyperelliptic superspecial curve of genus $4$ over ${\mathbb{F}}_{11}$. Our algorithm determining automorphism groups works for any nonhyperelliptic curves of genus $4$ over finite fields. With this computation, we show the compatibility between the enumeration of superspecial curves of genus $4$ over ${\mathbb{F}}_{11}$ obtained computationally by the first and second authors in 2017 and an enumeration by Galois cohomology theory.

References in corpus (2)

• Superspecial curves of genus $4$ in small characteristic
• Enumerating superspecial curves of genus $4$ over prime fields

Cited by in corpus (3)

• Enumerating superspecial curves of genus $4$ over prime fields
• Representation of non-special curves of genus 5 as plane sextic curves and its application to finding curves with many rational points
• Superspecial trigonal curves of genus $5$