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Quantum Singularity Theory for $A_{(r - 1)}$ and $r$ -Spin Theory

Huijun Fan; Tyler Jarvis; Yongbin Ruan — 2011

Annales de l’institut Fourier

We give a review of our construction of a cohomological field theory for quasi-homogeneous singularities and the $r$ -spin theory of Jarvis-Kimura-Vaintrob. We further prove that for a singularity $W$ of type $A$ our construction of the stack of $W$ -curves is canonically isomorphic to the stack of $r$ -spin curves described by Abramovich and Jarvis. We further prove that our theory satisfies all the Jarvis-Kimura-Vaintrob axioms for an $r$ -spin virtual class. Therefore, the Faber-Shadrin-Zvonkine proof of the...

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Quantum Singularity Theory for A ( r - 1 ) and r -Spin Theory

Quantum Singularity Theory for $A_{(r - 1)}$ and $r$ -Spin Theory