Constructions of nontautological classes on moduli spaces of curves

Abstract

We construct explicit examples of algebraic cycles in \bar M_g (for large g congruent to 2 mod 4) and in M_2,20 (no bar) which are not in the tautological ring. In an appendix we give a general method for computing intersections in the tautological ring.

This supersedes our earlier preprint, "A non-tautological algebraic class on ${\bar{M}}_{2,22}$." This version gives more general constructions of nontautological classes on various moduli spaces of pointed curves

References in corpus (1)

• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves

Cited by in corpus (20)

• Tautological relations and the r-spin Witten conjecture
• Stable pair, tropical, and log canonical compact moduli of del Pezzo surfaces
• Holomorphic anomaly equations and the Igusa cusp form conjecture
• admcycles -- a Sage package for calculations in the tautological ring of the moduli space of stable curves
• The Gorenstein conjecture fails for the tautological ring of ${\bar{\mathcal{M}}}_{2,n}$
• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$
• Relations on Mbar_{g,n} via 3-spin structures
• Tautological relations in moduli spaces of weighted pointed curves
• Twisted Gromov-Witten r-spin potential and Givental's quantization
• Tautological relations via r-spin structures
• Calculating intersection numbers on moduli spaces of pointed curves
• The Chen-Ruan cohomology of moduli of curves of genus 2 with marked points
• The Chern character of the Verlinde bundle over the moduli space of stable curves
• Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures
• Pixton's formula and Abel-Jacobi theory on the Picard stack
• Relative virtual localization and vanishing of tautological classes on moduli spaces of curves
• Topological recursion relations from Pixton's formula
• Cohomological field theories with non-tautological classes
• Tevelev degrees and Hurwitz moduli spaces
• On the rationality of moduli spaces of pointed curves