A. Kabanov et T. Kimura, INTERSECTION-NUMBERS AND RANK-ONE COHOMOLOGICAL FIELD-THEORIES IN GENUS ONE, Communications in Mathematical Physics, 194(3), 1998, pp. 651-674
We obtain a simple recursive presentation of the tautological (kappa,
psi, and lambda) classes on the moduli space of curves in genus 0 and
1 in terms of boundary strata (graphs). We derive differential equatio
ns for the generating functions for their intersection numbers which a
llow us to prove a simple relationship between the genus zero and genu
s one potentials. As an application, we describe the moduli space of n
ormalized, restricted, rank one cohomological field theories in genus
one in coordinates which are additive under taking tensor products. Ou
r results simplify and generalize those of Kaufmann, Manin, and Zagier
.