Non-tautological Hurwitz cycles

Carl Lian

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arXiv · 2101.11050

Non-tautological Hurwitz cycles

Carl Lian

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Abstract

We show that various loci of stable curves of sufficiently large genus admitting degree $d$ covers of positive genus curves define non-tautological algebraic cycles on $\overline{\mathcal{M}}_{g,N}$, assuming the non-vanishing of the $d$-th Fourier coefficient of a certain modular form. Our results build on those of Graber-Pandharipande and van Zelm for degree 2 covers of elliptic curves; the main new ingredient is a method to intersect the cycles in question with boundary strata, as developed recently by Schmitt-van Zelm and the author.

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Carl Lian. 2021-01-26. Non-tautological Hurwitz cycles. https://arxiv.org/abs/2101.11050

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