Elba Garcia-Failde, Reinier Kramer, Danilo Lewański, Sergey Shadrin, “Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes”, SIGMA, 2019, Volume 15,080, 27 pp.

This article is cited in 2 papers

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

Elba Garcia-Failde^a, Reinier Kramer^b, Danilo Lewański^b, Sergey Shadrin^c

^a Institute de Physique Théorique, CEA Paris-Saclay, Orme des Merisiers, 91191 Gif-sur-Yvette, France
^b Max Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
^c Korteweg-de Vries Instituut voor Wiskunde, Universiteit van Amsterdam, Postbus 94248, 1090GE Amsterdam, The Netherlands

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 $\mathcal{M}_g$, $g\geq 2$. We then prove several cases of the combinatorial identity, providing a new proof of Faber's formula for those cases.

Keywords: tautological ring, tautological relations, moduli spaces of curves, Faber intersection number conjecture, odd-even binomial coefficients.

MSC: 14H10, 05A10

Received: June 19, 2019; in final form October 14, 2019; Published online October 18, 2019

Language: English

DOI: 10.3842/SIGMA.2019.080