The chiral de rham complex and positivity of the equivariant signatures of some loop spaces

In this note we show that the positivity property of the equivariant signature of the loop space, first observed in MS1] in the case of the even-dimensional projective spaces, is valid for Picard number 2 toric varieties. A new formula for the equivariant signature of the loop space in the case of a toric spin variety is derived.Partially supported by an NSF grant