Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes

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.