Quaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds
| dc.creator | Verbitsky, Misha | |
| dc.date | 2006-04-13 | |
| dc.date | 2006-09-16 | |
| dc.date.accessioned | 2026-07-07T09:26:39Z | |
| dc.date.available | 2026-07-07T09:26:39Z | |
| dc.description | Let (M,I,J,K) be a hyperkahler manifold of real dimension 4n, and L a non-trivial holomorphic line bundle on (M,I). Using the quaternionic Dolbeault complex, we prove the following vanishing theorem for holomorphic cohomology of L. If the Chern class c_1(L) lies in the closure $\hat K$ of the dual Kahler cone, then $H^i(L)=0$ for i>n. If c_1(L) lies in the opposite cone $-\hat K$, then $H^i(L)=0$ for i<n. Finally, if $c_1(L)$ is neither in $\hat K$ nor in $-\hat K$, then $H^i(L)=0$ for $i\neq n$. | |
| dc.description | 30 pages, version 2 - misprints corrected, some arguments improved | |
| dc.identifier | https://arxiv.org/abs/math/0604303 | |
| dc.identifier | http://arxiv.org/abs/math/0604303 | |
| dc.identifier | Compos. Math. 143 (2007), no. 6, 1576--1592 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156824 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 53C26 | |
| dc.title | Quaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds | |
| dc.type | text |