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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 080, 27 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.080 (Mi sigma1516) 		 
This article is cited in 2 scientific papers (total in 2 papers)

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

Elba Garcia-Faildea, Reinier Kramerb, Danilo Lewańskib, Sergey Shadrinc

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
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DOI: https://doi.org/10.3842/SIGMA.2019.080
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.
Funding agency Grant number
Netherlands Organization for Scientific Research
Fondation Mathématique Jacques Hadamard
R.K., D.L., and S.S. were supported by the Netherlands Organization for Scientific Research. D.L. was also supported by the Max Planck Gesellschaft. E.G.-F. was supported by the Max Planck Gesellschaft and by the Labex Mathematics Hadamard.
Received: June 19, 2019; in final form October 14, 2019; Published online October 18, 2019
Bibliographic databases:
Document Type: Article
MSC: 14H10, 05A10
Language: English
Citation: Elba Garcia-Failde, Reinier Kramer, Danilo Lewański, Sergey Shadrin, “Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes”, SIGMA, 15 (2019), 080, 27 pp.
Citation in format AMSBIB
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\paper Half-Spin Tautological Relations and Faber's Proportionalities of Kappa Classes
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\vol 15
\papernumber 080
\totalpages 27
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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