Nontautological bielliptic cycles

Jason van Zelm
2018 Pacific Journal of Mathematics  
Let $[\overline{\mathcal{B}}_{2,0,20}]$ and $[\mathcal{B}_{2,0,20}]$ be the classes of the loci of stable resp. smooth bielliptic curves with 20 marked points where the bielliptic involution acts on the marked points as the permutation (1 2)...(19 20). Graber and Pandharipande proved that these classes are nontatoulogical. In this note we show that their result can be extended to prove that $[\overline{\mathcal{B}}_{g}]$ is nontautological for $g\geq 12$ and that $[\mathcal{B}_{12}]$ is
more » ... }_{12}]$ is nontautological.
doi:10.2140/pjm.2018.294.495 fatcat:bo6a6adezzeivetzu35cvlfwwq