We employ the 1/2-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on Mg, g ≥ 2. We then prove several cases of the combinatorial identity, providing a new proof of Faber's formula for those cases.
Garcia-Failde, E., Kramer, R., Lewanski, D., Shadrin, S. (2019). Half-spin tautological relations and Faber's proportionalities of kappa classes. SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS, 15 [10.3842/SIGMA.2019.080].
Half-spin tautological relations and Faber's proportionalities of kappa classes
Kramer R.;
2019
Abstract
We employ the 1/2-spin tautological relations to provide a particular combinatorial identity. We show that this identity is a statement equivalent to Faber's formula for proportionalities of kappa-classes on Mg, g ≥ 2. We then prove several cases of the combinatorial identity, providing a new proof of Faber's formula for those cases.
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