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.
We show that for infinite measure-preserving transformations, power weak mixing does not imply multiple recurrence. We also show that the infinite measure-preserving " Chacon transformation " known to have infinite ergodic index is not power weakly mixing, and is 3-recurrent but not multiply recurrent. We also construct some doubly ergodic infinite… (More)
We define the singular orbifold elliptic genus and E-function for all normal surfaces without strictly log-canonical singularities, and prove the analogue of the McKay correspondence in this setting. Our invariants generalize the stringy invariants defined by Willem Veys for this class of singularities. We show that the ability to define these in-variants… (More)
In this paper we prove an equivariant version of the McKay correspondence for the elliptic genus on open varieties with a torus action. As a consequence, we will prove the equivariant DMVV formula for the Hilbert scheme of points on C 2 .
A differential operator D commuting with an S 1-action is said to be rigid if the non-constant Fourier coefficients of ker D and coker D are the same. Somewhat surprisingly, the study of rigid differential operators turns out to be closely related to the problem of defining Chern numbers on singular varieties. This relationship comes into play when we make… (More)
We define the singular elliptic genus for arbitrary normal surfaces, prove that it is a birational invariant, and show that it generalizes the singular elliptic genus of Borisov and Libgober and the stringy χy genus of Batyrev and Veys.
Biographical information regarding Robert Waelder is readily available (Guttman, 1986), and this is not the place for it. The following is a rare and direct example of his "old-fashioned" teaching. "Old-fashioned" and "conservative" are criticisms often leveled at Waelder these days. Yet, "Old-fashioned is not precisely the word for Waelder.... He was a… (More)