Iterated residue, toric forms and Witten genus

TL;DR

This paper introduces iterated residues to analyze generalized Bott manifolds, leading to new vanishing results, theta function identities, and a twisted Rogers-Ramanujan formula for certain toric varieties.

Contribution

It presents a novel application of iterated residues to compute toric forms and the Witten genus, revealing new identities and vanishing phenomena in toric geometry.

Findings

Derived vanishing results for toric forms and Witten genus

Established new theta function identities including a twisted Rogers-Ramanujan formula

Connected iterated residues with geometric invariants of toric varieties

Abstract

We introduce the notion of {\em iterated residue} to study generalized Bott manifolds. When applying the iterated residues to compute the Borisov-Gunnells toric form and the Witten genus of certain toric varieties as well as complete intersections, we obtain interesting vanishing results and some theta function identities, one of which is a twisted version of a classical Rogers-Ramanujan type formula.