Equivariant elliptic genera

Abstract

We introduce the equivariant elliptic genus for open varieties and prove an equivariant version of the change of variable formula for blow-ups along complete intersections. In addition, we prove the equivariant elliptic genus analogue of the McKay correspondence for the ALE spaces.

Equivariant Elliptic Genera and Local McKay Correspondences

“…The above formula follows from theorem 7 of the preprint [17] or by lemma 8.1 of [7]. This completes the proof.…”

“…Later it became apparant that the proof given in [17] could be adapted to the case in which X was a "normal cone space", i.e., a fiber product of spaces P(F ⊕ 1), where F → W was a holomorphic vectorbundle. The idea was that the Chern roots of the tautological quotient bundle Q F → X should play the role of the "divisors" in a polyhedral complex associated to X.…”

“…We next discuss the equivariant elliptic genus analogue of the classical McKay correspondence, which was originally proved in [17]. Let G ⊂ SU (2) be a finite subgroup.…”

Higher elliptic genera

“…Case of higher one variable elliptic genus is discussed in [24] and [15] (cf. also [29]). b) One has a version of higher elliptic genera twisted by discrete torsion extending the one considered in [23].…”

Equivariant Hirzebruch Classes and Molien Series of Quotient Singularities

“…The straight-forward verification of the formula (18) in the equivariant context was done in [Wae08a]. The equivariant counterpart of McKay correspondence for elliptic genus, i.e., the equivariant version of Theorem 12, was proved in [Wae08b].…”