A Combinatorial Algorithm Related to the Geometry of the Moduli Space of Pointed Curves
G. Bini
DOI: 10.1023/A:1015025306777
Abstract
As pointed out in Arbarello and Cornalba ( J. Alg. Geom. 5 (1996), 705-749), a theorem due to Di Francesco, Itzykson, and Zuber (see Di Francesco, Itzykson, and Zuber, Commun. Math. Phys. 151 (1993), 193-219) should yield new relations among cohomology classes of the moduli space of pointed curves. The coefficients appearing in these new relations can be determined by the algorithm we introduce in this paper.
Pages: 211–221
Keywords: Schur Q-polynomials; projective representations; moduli space of curves
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References
1. E. Arbarello and M. Cornalba, “Combinatorial and algebro geometric cohomology classes on the moduli space of curves,” J. Alg. Geom. 5 (1996), 705-749.
2. D. Bessis, C. Itzykson, and J.B. Zuber, “Quantum field theory techniques in graphical enumeration,” Adv. Appl. Math. 1 (1980), 109-157.
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2. D. Bessis, C. Itzykson, and J.B. Zuber, “Quantum field theory techniques in graphical enumeration,” Adv. Appl. Math. 1 (1980), 109-157.
3. P. Di Francesco, C. Itzykson, and J.-B. Zuber, “Polynomial averages in the Kontsevich model,” Commun. Math. Phys. 151 (1993), 193-219.
4. C. Faber, “A conjectural description of the tautological ring of the moduli space of curves,” in Moduli of Curves and Abelian Varieties, The Dutch Intercity Seminar on Moduli, C. Faber and E. Looijenga (Eds.), Aspects of Maths. E 33, Vieweg, 1999.
5. T. Jósefiak, “Symmetric functions in the Kontsevich-Witten intersection theory of the moduli space of curves,” Letters in Mathematical Physics 33 (1995), 347-351.
6. M. Kontsevich, “Intersection theory on the moduli space of curves and the matrix Airy function,” Commun. Math. Phys. 147 (1992), 1-23.
7. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Clarendon Press, Oxford, 1979.
8. I. Schur, “ \ddot Uber die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare Substitutionem,” J. Reine Angew. Math 139 (1911), 155-250.
9. E. Witten, “Two dimensional gravity and intersection theory on moduli space,” Survey in Diff. Geom. 1 (1991), 243-310.