Intersection Numbers and Rank One Cohomological Field Theories in Genus One

Details Intersection Numbers and Rank One Cohomological Field Theories in Genus One Intersection Numbers and Rank One Cohomological Field Theories in Genus One

1997-06-05

arxiv.org/abs/alg-geom/9706003v2

Commun.Math.Phys. 194 (1998) 651-674

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX2e, 31 pages, 15 postscript figs; Minor changes in revised version

Scientific paper

10.1007/s002200050373

We obtain a simple, recursive presentation of the tautological (\kappa, \psi, and \lambda) classes on the moduli space of curves in genus zero and one in terms of boundary strata (graphs). We derive differential equations for the generating functions for their intersection numbers which allow us to prove a simple relationship between the genus zero and genus one potentials. As an application, we describe the moduli space of normalized, even, rank one cohomological field theories in genus one in coordinates which are additive under taking tensor products. Our results simplify and generalize those of Kaufmann, Manin, and Zagier.

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