Nontautological bielliptic cycles

Jason van Zelm

Vol. 294 (2018), No. 2, 495–504

DOI: 10.2140/pjm.2018.294.495

Abstract

Let $\left[{\overline{\mathcal{ℬ}}}_{2,0,20}\right]$ and $\left[{\mathcal{ℬ}}_{2,0,20}\right]$ respectively be the classes of the loci of stable and of smooth bielliptic curves with $20$ marked points where the bielliptic involution acts on the marked points as the permutation $\left(12\right)\cdots \left(1920\right)$. Graber and Pandharipande proved that these classes are nontautological. In this note we show that their result can be extended to prove that $\left[{\overline{\mathcal{ℬ}}}_g\right]$ is nontautological for $g\ge 12$ and that $\left[{\mathcal{ℬ}}_{12}\right]$ is nontautological.

Keywords

nontautological, bielliptic

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14H30, 14H37

Milestones

Received: 7 December 2016

Revised: 18 October 2017

Accepted: 15 December 2017

Published: 20 February 2018