On Regularized Elliptic Genera of ALE Spaces
Jian Zhou
TL;DR
This paper introduces a regularization method for elliptic genera of ALE spaces of type A, revealing their proportionality to the elliptic genus of K3 surfaces, thus connecting geometric invariants.
Contribution
It defines regularized elliptic genera for ALE spaces of type A via nonequivariant limits, establishing a new link to K3 surface elliptic genera.
Findings
Regularized elliptic genera are multiples of K3 elliptic genus.
The approach involves taking limits of equivariant elliptic genera.
The results connect ALE space invariants to well-known K3 invariants.
Abstract
We define regularized elliptic genera of ALE space of type A by taking some regularized nonequivariant limits of their equivariant elliptic genera with respect to some torus actions. They turn out to be multiples of the elliptic genus of a K3 surface.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds