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We employ the $1/2$-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Fabers formula for proportionalities of kappa-classes on $mathcal{M}_g$, $ggeq 2$. We then prove several cases of the combinatorial identity, providing a new proof of Fabers formula for those cases.
We prove that a curious generating series identity implies Fabers intersection number conjecture (by showing that it implies a combinatorial identity already given in arXiv:1902.02742) and give a new proof of Fabers conjecture by directly proving this identity.
Relations among tautological classes on the moduli space of stable curves are obtained via the study of Wittens r-spin theory for higher r. In order to calculate the quantum product, a new formula relating the r-spin correlators in genus 0 to the rep
This note is an erratum to the paper Tautological classes on moduli spaces of hyper-Kahler manifolds. Thorsten Beckman and Mirko Mauri have pointed to us a gap in the proof of cite[Theorem 8.2.1]{Duke}. We do not know how to correct the proof. We can
In this paper, we discuss the cycle theory on moduli spaces $cF_h$ of $h$-polarized hyperkahler manifolds. Firstly, we construct the tautological ring on $cF_h$ following the work of Marian, Oprea and Pandharipande on the tautological conjecture on m
A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological cohomology o