Quaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds

dc.creatorVerbitsky, Misha
dc.date2006-04-13
dc.date2006-09-16
dc.date.accessioned2026-07-07T09:26:39Z
dc.date.available2026-07-07T09:26:39Z
dc.descriptionLet (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.description30 pages, version 2 - misprints corrected, some arguments improved
dc.identifierhttps://arxiv.org/abs/math/0604303
dc.identifierhttp://arxiv.org/abs/math/0604303
dc.identifierCompos. Math. 143 (2007), no. 6, 1576--1592
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156824
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.subject53C26
dc.titleQuaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds
dc.typetext

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