Integrals of ψ-classes over double ramification cycles

By A. Buryak, Sergey Shadrin, L. Spitz, Dimitri Zvonkine. 2012

65 citations recorded by the source corpus.

A double ramification cycle, or DR-cycle, is a codimension $g$ cycle in the moduli space $\overline{\mathcal M}_{g,n}$ of stable curves. Roughly speaking, given a list of integers $(a_1,\ldots,a_n)$, the DR-cycle ${\rm DR}_g(a_1,\ldots,a_n) \subset\overline{\mathcal M}_{g,n}$ is the locus of curves $(C,x_1,\ldots,x_n)$ such that the divisor $\sum a_ix_i$ is principal. We compute the intersection numbers of DR-cycles with all monomials in $\psi$-classes.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/9ee01f8c5dbba34d08b4199742027c3023df8f19

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In Algebra and Number Theory

1. Dimitri Zvonkine
2. R. Pandharipande
3. A. Okounkov
4. K. Costello
5. Nick Scott
6. Paul T. Norbury

In Discrete Mathematics and Combinatorics

1. Aaron Pixton
2. Dimitri Zvonkine
3. R. Pandharipande
4. A. Okounkov
5. Yukinobu Toda
6. K. Costello

In Geometry and Topology

1. Aaron Pixton
2. Dimitri Zvonkine
3. R. Pandharipande
4. F. Janda
5. A. Okounkov
6. Davesh Maulik
7. Yukinobu Toda
8. Richard P. Thomas

Citations in the corpus

• Double ramification cycles on the moduli spaces of curves (2016, background): “Shadows of the polynomiality of the double ramification cycle were proven earlier in [3, 29].”