A note on some Picard curves over finite fields

Kazemifard, Ahmad; Tafazolian, Saeed

doi:10.1016/j.ffa.2014.12.002

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2021

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“…From Theorems A and B, we can also determine the Newton polygon and the Ekedahl-Oort type of every curve C of genus 3 with Aut(C) = Z 6 or Z 9 , see Section 5 for details. Note that we used the result [13,Theorem 3.2] by Kazemifard and Tafazolian on the Newton polygon of the curve C with Aut(C) = Z 9 .…”

Section: Introductionmentioning

confidence: 99%

The $a$-numbers of non-hyperelliptic curves of genus three with large cyclic automorphism group

Ohashi¹,

Kudo²,

Harashita³

2021

Preprint

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In the study of algebraic curves and their moduli spaces, it is important to determine the a-numbers of curves over a field of positive characteristic. It is known that non-hyperelliptic curves of genus 3 are classified by the structures of their automorphism groups as finite groups. In this paper, we determine the a-numbers of non-hyperelliptic curves of genus 3 with cyclic automorphism group of order 6 or 9. Moreover, we also find the exact number of the isomorphism classes of such curves attaining the possible maximal a-number.

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Section: Introductionmentioning

confidence: 99%