Constructions of nontautological classes on moduli spaces of curves
By T. Graber, R. Pandharipande. 2001
153 citations recorded by the source corpus.
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.
View Paper: https://www.semanticscholar.org/paper/5d7d9d61315205ac7ba44f19fede8e157dd7ec06
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
- R. Pandharipande
- Aaron Pixton
- Carel Faber
- G. Farkas
- Davesh Maulik
- A. Okounkov
- Dawei Chen
- Yukinobu Toda
Citations in the corpus
- Tautological and non-tautological cohomology of the moduli space of curves (2011, background): “cal boundary terms plays a crucial role in the argument. 0.4. Boundary geometry. The existence of non-tautological cohomology classes of Hodge type was earlier established by Graber and Pandharipande [35]. In particular, an explicit such class in the boundary of M2,22 was found. In Section 5, we rev”
- Relative maps and tautological classes (2003, methodology): “ven stratum by products of ψand κclasses, valY(v) i=1 ψa i i Y j≥0 κb j j , 37 at each vertex vof the dual graph. Every tautological boundary class is a linear combination of these basic classes (see [GrP2]). By Proposition 2, we may require the condition (26) valX(v) i=1 ai + X j≥0 jbj <g(v) +δ ”
- Relations on Mbar_{g,n} via 3-spin structures (2013, unknown): “More precisely, the set of edges E of Γ should be represented as a union of two (not necessarily disjoint) subsets, in such a way that Γ 1 is obtained by contracting all the edges outside E 1 and Γ 2 is obtained by contracting all edges outside E 2 (see Proposition 9 in the Appendix of [8]).”
- Relations in the tautological ring of the moduli space of curves (2013, background): “If these bounds agree with the Gorenstein ranks (which are computed by implementing the multiplication rule described in [17]), then the result is that the tautological cohomology ring is Gorenstein and all relations are given by our conjectured list of relations.”
- THE MODULI SPACE OF TWISTED CANONICAL DIVISORS (2015, background): “For a review of κ and and the cotangent ψ classes, see [15].”