On the generic curve of genus 3
On the generic curve of genus 3
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在属 3 的通用曲线上
DOI：
10.1090/conm/369/06814
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发表时间：
2012
期刊：
影响因子：
--
通讯作者：
J. Thompson
中科院分区：
文献类型：
--
作者：
T. Shaska;J. Thompson
We study genus $g$ coverings of full moduli dimension of degree $d=[\frac {g+3} 2]$. There is a homomorphism between the corresponding Hurwitz space $\H$ of such covers to the moduli space $\M_g$ of genus $g$ curves. In the case $g=3$, using the signature of such covering we provide an equation for the generic ternary quartic. Further, we discuss the degenerate subloci of the corresponding Hurwitz space of such covers from the computational group theory viewpoint. In the last section, we show that one of these degenerate loci corresponds to the locus of curves with automorphism group $C_3$. We give necessary conditions in terms of covariants of ternary quartics for a genus 3 curve to belong to this locus.
