Relations in the tautological ring of the moduli space of curves
By R. Pandharipande, Aaron Pixton. 2013
50 citations recorded by the source corpus.
The virtual geometry of the moduli space of stable quotients is used to obtain Chow relations among the kappa classes on the moduli space of nonsingular genus g curves. In a series of steps, the stable quotient relations are rewritten in successively simpler forms. The final result is the proof of the Faber-Zagier relations (conjectured in 2000).
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c2d1fc3e04042e2080c7e4dc0ec9e3736885fce5
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In Geometry and Topology
- R. Pandharipande
- D. Oprea
- Aaron Pixton
- Dimitri Zvonkine
- A. Marian
- F. Janda
- A. Okounkov
- Davesh Maulik
In Mathematical Physics
- R. Pandharipande
- D. Oprea
- Aaron Pixton
- A. Marian
- Dimitri Zvonkine
- F. Janda
- A. Okounkov
- Davesh Maulik
Citations in the corpus
- Double ramification cycles on the moduli spaces of curves (2016, background): “ructure of the tautological rings1 R∗(M g,n) ⊂A∗(Mg,n) of the moduli spaces of curves. We refer the reader to [12] for a survey of the basic definitions and properties of R∗(M g,n). The recent results [22, 33, 34] concerning relations in R∗(M g,n), conjectured to be all relations [35], may be viewed ”
- Segre classes and Hilbert schemes of points (2015, result): “urve may be pursued in a virtual sense for a fixed curve [15] or by letting the curve vary via the moduli space of stable quotients [16]. The relations in the tautological ring of the moduli of curves [11, 21, 22] via virtual localization on the moduli stable quotients are parallel to the relations w”
- Relations on Mbar_{g,n} via 3-spin structures (2013, unknown): “A proof of the Faber-Zagier conjecture (in Chow) via the geometry of stable quotients was given in 2010 [14].”