Intersection numbers and automorphisms of stable curves

Details Intersection numbers and automorphisms of stable curves Intersection numbers and automorphisms of stable curves

2006-08-09

arxiv.org/abs/math/0608209v5

Michigan Math. J. 58 (2009), no. 2, 385--400

Mathematics

Algebraic Geometry

12 pages, to appear in Michigan Math. J

Scientific paper

Due to the orbifold singularities, the intersection numbers on the moduli space of curves $\bar{\sM}_{g,n}$ are in general rational numbers rather than integers. We study the properties of the denominators of these intersection numbers and their relationship with the orders of automorphism groups of stable curves. In particular, we prove a conjecture of Itzykson and Zuber. We also present a conjectural multinomial type numerical property for Hodge integrals.

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