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A new proof of Faber's intersection number conjecture

A. Buryak, S. Shadrin

Abstract

We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves $\M_g$. The proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles.

A new proof of Faber's intersection number conjecture

Abstract

We give a new proof of Faber's intersection number conjecture concerning the top intersections in the tautological ring of the moduli space of curves . The proof is based on a very straightforward geometric and combinatorial computation with double ramification cycles.

Paper Structure

This paper contains 21 sections, 18 theorems, 62 equations.

Table of Contents

  1. Introduction
  2. Notations
  3. Faber's conjecture
  4. Top intersections
  5. Double ramification cycles
  6. Organization of the paper
  7. Acknowledgements
  8. Integrals over DR-cycles
  9. Reduction to initial DR-cycles
  10. Expression for a $\psi$-class on the initial cycle
  11. Initial values
  12. Basic properties of integrals over DR-cycles
  13. A small simplification
  14. Polynomiality
  15. Divisibility
  16. ...and 6 more sections

Key Result

Lemma 2.1

In $R^0({\mathcal{M}}^{rt}_{g,1+n})$ we have:

Theorems & Definitions (38)

  • Lemma 2.1
  • Lemma 2.2
  • proof : Sketch of proofs
  • Proposition 2.3
  • proof : Sketch of a proof
  • Proposition 2.4
  • proof : Sketch of a proof
  • Proposition 2.5
  • proof : Sketch of a proof
  • Lemma 3.1
  • ...and 28 more