Counting the number of trigonal curves of genus 5 over finite fields

被引：3

作者：

Wennink, Thomas ^{[1
]}

机构：

[1] Univ Liverpool, Liverpool, Merseyside, England

来源：

GEOMETRIAE DEDICATA | 2020年 / 208卷 / 01期

关键词：

Moduli space of curves; Trigonal curves; Plane curves; Finite fields; Trace of Frobenius; MODULI SPACES; POLYNOMIALS; COHOMOLOGY; POINTS;

D O I：

10.1007/s10711-019-00508-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The trigonal curves of genus 5 can be represented by projective plane quintics that have one singularity of delta invariant one. Combining this with a partial sieve method for plane curves we count the number of such curves over any finite field. The main application is that this gives the motivic Euler characteristic of the moduli space of trigonal curves of genus 5.

引用

页码：31 / 48

页数：18

共 11 条

[1]

Arbarello E., 1984, Geometry of Algebraic Curves: Volume 1, V1

[2]

Bergstrom J., UNPUB

[3] Cohomology of moduli spaces of curves of genus three via point counts [J].