Witten genera of complete intersections

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.

minor changes in v2, to appear in the Bulletin of the LMS

References in corpus (3)

• A note on torus actions and the Witten genus
• Curvature operators and rational cobordism
• On a conjecture of Stolz in the toric case