#### Vol. 294, No. 2, 2018

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Nontautological bielliptic cycles

### Jason van Zelm

Vol. 294 (2018), No. 2, 495–504
##### Abstract

Let $\left[{\overline{\mathsc{ℬ}}}_{2,0,20}\right]$ and $\left[{\mathsc{ℬ}}_{2,0,20}\right]$ 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 $\left(1\phantom{\rule{2.77626pt}{0ex}}2\right)\cdots \left(19\phantom{\rule{2.77626pt}{0ex}}20\right)$. Graber and Pandharipande proved that these classes are nontautological. In this note we show that their result can be extended to prove that $\left[{\overline{\mathsc{ℬ}}}_{g}\right]$ is nontautological for $g\ge 12$ and that $\left[{\mathsc{ℬ}}_{12}\right]$ 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
##### Authors
 Jason van Zelm Department of Mathematical Sciences University of Liverpool Liverpool United Kingdom