Elliptic genera, torus manifolds and multi-fans
| dc.creator | Hattori, Akio | |
| dc.creator | Masuda, Mikiya | |
| dc.date | 2001-07-03 | |
| dc.date | 2004-12-13 | |
| dc.date.accessioned | 2026-07-07T06:22:29Z | |
| dc.date.available | 2026-07-07T06:22:29Z | |
| dc.description | The rigidity theorem of Witten-Bott-Taubes-Hirzebruch tells us that, if the circle group acts on a closed almost complex (or more generally unitary) manifold whose first Chern class is divisible by a positive integer N greater than 1, then its equivariant elliptic genus of level N is rigid. Applying this to a non-singular compact toric variety, we see that its elliptic genus of level N is rigid if its first Chern class is divisible by N. But, using a vanishing theorem of Hirzebruch, we can show moreover that the genus actually vanishes. In this note we shall extend this result to torus manifolds. In fact, a non-singular complete multi-fan is associated with a torus manifold, and rigidity and vanishing of elliptic genus of level N can be formulated and proved for non-singular complete multi-fans. Some applications on compact non-singular toric varieties with the first Chern class divisible by a large positive integer are given. | |
| dc.identifier | https://arxiv.org/abs/math/0107014 | |
| dc.identifier | http://arxiv.org/abs/math/0107014 | |
| dc.identifier | Internat. J. of Math. 16 (2005), no.9, 957--998 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/95925 | |
| dc.subject | Symplectic Geometry | |
| dc.subject | Algebraic Topology | |
| dc.title | Elliptic genera, torus manifolds and multi-fans | |
| dc.type | text |