Tautological classes on the moduli space of hyperelliptic curves with rational tails
Journal of Pure and Applied Algebra | ELSEVIER SCIENCE BV | Published : 2018
We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology.
I would like to thank Gabriel C. Drummond-Cole, Carel Faber, Gerard van der Geer, Richard Hain, Robin de Jong, Felix Janda, Nicola Pagani, Aaron Pixton and Orsola Tommasi for the valuable discussions and their comments. Special thanks are due to Qizheng Yin for useful discussions and corrections. This research was started during my stay at the Max-Planck-Institut fur Mathematik and was completed at the university of Amsterdam. Thanks to Sergey Shadrin for his interest in this project and his support. I was supported by the research grant IBS-R003-S1.