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Invariance of tautological equations. I: Conjectures and applications. (English) Zbl 1170.14021
The author introduces some conjectures on the relations in the tautological rings. These rings are subrings of $$A^{*}(\overline{M}_{g,n})$$ or $$H^{2*}(\overline{M}_{g,n})$$ , where $$\overline{M}_{g,n}$$ is the moduli stack of stable curves.
The techniques presented here give an algorithm to calculate all tautological equations using finite dimensional linear algebra. One can also apply them towards the proofs of Witten’s and Virasoro’s conjectures.

##### MSC:
 14H10 Families, moduli of curves (algebraic) 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
##### Keywords:
tautological rings; Chow rings; tautological equations
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##### References:
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