EQUIVARIANT SHORT EXACT SEQUENCES OF VECTOR-BUNDLES AND THEIR ANALYTIC-TORSION FORMS

In this paper, we construct analytic torsion forms associated to a short exact sequence of holomorphic Hermitian vector bundles equipped with a holomorphic unitary endomorphism g, thus extending results of a previous paper where the case g = 1 was considered. We calculate these forms explicitly, in terms of an additive equivariant genus D(0, x). We introduce a related additive equivariant genus R(0, x), which for 0 = 0, coincides with the genus R(x) of Gillet and Soule By comparison with explicit computations by Gillet-Soule and Kohler of the Ray-Singer analytic torsion of projective spaces, we conjecture a formula of Riemann-Roch in equivariant Arakelov geometry, in which the genus R(0, x) appears explicitly.