Witten genera of complete intersections

TL;DR

This paper establishes vanishing results for Witten genera in certain Spin^c-manifolds, providing new evidence for Stolz's conjecture, especially in the context of Fano manifolds with specific topological properties.

Contribution

It introduces new vanishing theorems for Witten genera of string generalized complete intersections within Spin^c-manifolds, advancing understanding of their geometric and topological properties.

Findings

Vanishing of Witten genera in string generalized complete intersections.

Application of results to Fano manifolds with second Betti number one.

Support for Stolz's conjecture in specific geometric contexts.

Abstract

We prove vanishing results for Witten genera of string generalized complete intersections in homogeneous $\text{Spin}^c$-manifolds and in other $\text{Spin}^c$-manifolds with Lie group actions. By applying these results to Fano manifolds with second Betti number equal to one we get new evidence for a conjecture of Stolz.