scholarly journals Dolbeault Complex on S4\{·} and S6\{·} through Supersymmetric Glasses

2011 ◽  
Author(s):  
Andrei V. Smilga
Keyword(s):  
Dolbeault Complex

scholarly journals A NEW DOLBEAULT COMPLEX IN QUATERNIONIC AND CLIFFORD ANALYSIS

2009 ◽  
Author(s):  
F. COLOMBO ◽  
I. SABADINI ◽  
A. DAMIANO ◽  
D. C. STRUPPA
Keyword(s):  
Clifford Analysis ◽  
Dolbeault Complex

scholarly journals Quaternionic Dolbeault complex and vanishing theorems on hyperkähler manifolds

2007 ◽  
Vol 143 (6) ◽  
pp. 1576-1592 ◽  
Author(s):  
Misha Verbitsky
Keyword(s):  
Line Bundle ◽  
Holomorphic Line Bundle ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Hyperkähler Manifolds ◽  
Hyperkähler Manifold ◽  
Dolbeault Complex

AbstractLet (M,I,J,K) be a compact hyperkähler manifold, $\dim _{\mathbb {H}}M=n$, 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 c1(L) lies in the closure $\hat K$ of the dual Kähler cone, then Hi(L)=0 for i>n. If c1(L) lies in the opposite cone $-\hat K$, then Hi(L)=0 for i<n. Finally, if c1(L) is neither in $\hat K$ nor in $-\hat K$, then Hi(L)=0 for $i\neq n$.

The Generalized Dolbeault Complex in Two Clifford Variables

2007 ◽  
Vol 17 (3) ◽  
pp. 537-548 ◽  
Author(s):  
Lukáš Krump ◽  
Vladimír Souček
Keyword(s):  
Dolbeault Complex
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