We prove that the rational cohomology Hi(Tg; Q) of the moduli space of trigonal curves of genus g is independent of g in degree i < [g/4]. This makes possible to define the stable cohomology ring as H•(Tg; Q) for a sufficiently large g. We also compute the stable cohomology ring, which turns out to be isomorphic to the tautological ring. This is done by studying the embedding of trigonal curves in Hirzebruch surfaces and using Gorinov–Vassiliev’s method.
Stable Cohomology of the Moduli Space of Trigonal Curves
ZHENG Angelina
2024
Abstract
We prove that the rational cohomology Hi(Tg; Q) of the moduli space of trigonal curves of genus g is independent of g in degree i < [g/4]. This makes possible to define the stable cohomology ring as H•(Tg; Q) for a sufficiently large g. We also compute the stable cohomology ring, which turns out to be isomorphic to the tautological ring. This is done by studying the embedding of trigonal curves in Hirzebruch surfaces and using Gorinov–Vassiliev’s method.
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