Vanishing theorems for L2 -cohomology groups

2000 ◽  
Vol 2000 (525) ◽  
pp. 95-112 ◽  
Author(s):  
J. Jost ◽  
Y. L. Yin
Keyword(s):  
Vanishing Theorems ◽  
Cohomology Groups ◽  
L2 Cohomology

scholarly journals A generalization of Kita and Noumi’s vanishing theorems of cohomology groups of local system

1997 ◽  
Vol 147 ◽  
pp. 63-69 ◽  
Author(s):  
Koji Cho
Keyword(s):  
Algebraic Geometry ◽  
Spectral Sequence ◽  
Local System ◽  
Vanishing Theorems ◽  
Vanishing Theorem ◽  
Cohomology Groups ◽  
De Rham

AbstractWe prove vanishing theorems of cohomology groups of local system, which generalize Kita and Noumi’s result and partially Aomoto’s result. Main ingredients of our proof are the Hodge to de Rham spectral sequence and Serre’s vanishing theorem in algebraic geometry.

scholarly journals REGULARITY AND RESOLUTIONS FOR MULTIGRADED MODULES

2007 ◽  
Vol 06 (04) ◽  
pp. 703-730
Author(s):  
JEROME W. HOFFMAN ◽  
HAOHAO WANG
Keyword(s):  
Local Cohomology ◽  
Free Resolutions ◽  
Vanishing Theorems ◽  
Cohomology Groups ◽  
Vanishing Of Cohomology ◽  
Multigraded Modules

This paper is concerned with the relationships between two concepts, vanishing of cohomology groups and the structure of free resolutions. In particular, we study the connection between vanishing theorems for the local cohomology of multigraded modules and the structure of their free multigraded resolutions.

scholarly journals ON VANISHING THEOREMS FOR LOCAL SYSTEMS ASSOCIATED TO LAURENT POLYNOMIALS

2017 ◽  
Vol 231 ◽  
pp. 1-22 ◽  
Author(s):  
ALEXANDER ESTEROV ◽  
KIYOSHI TAKEUCHI
Keyword(s):  
Morse Theory ◽  
Hypergeometric Functions ◽  
Vanishing Theorems ◽  
Cohomology Groups ◽  
Laurent Polynomials ◽  
Perverse Sheaves ◽  
Local Systems ◽  
Vanishing Cycles

We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand et al.[Generalized Euler integrals and$A$-hypergeometric functions, Adv. Math.84(1990), 255–271] to various directions. In the course of the proof, some properties of vanishing cycles of perverse sheaves and twisted Morse theory are used.

Vanishing theorems for the cohomology groups of free boundary submanifolds

2019 ◽  
Vol 56 (1) ◽  
pp. 137-146
Author(s):  
Marcos P. Cavalcante ◽  
Abraão Mendes ◽  
Feliciano Vitório
Keyword(s):  
Free Boundary ◽  
Vanishing Theorems ◽  
Cohomology Groups

VANISHING THEOREMS ON STRONGLY Q-CONVEX MANIFOLDS

2005 ◽  
Vol 02 (03) ◽  
pp. 467-483 ◽  
Author(s):  
O. ABDELKADER ◽  
S. SABER
Keyword(s):  
Vector Bundle ◽  
Convex Domain ◽  
Holomorphic Vector Bundle ◽  
Kähler Manifold ◽  
Vanishing Theorems ◽  
Cohomology Groups ◽  
Kahler Manifold

Let X be strongly q-convex domain of an n-dimensional Kähler manifold M and E be a holomorphic vector bundle over M. Then, if E satisfies certain positivity conditions, we prove vanishing theorems for the [Formula: see text]-cohomology groups of X with values in E.

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