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 Weakly normal varieties: The multicross singularity and some vanishing theorems on local cohomology

1975 ◽  
Vol 83 ◽  
pp. 137-152 ◽  
Author(s):  
John V. Leahy ◽  
Marie A. Vitulli
Keyword(s):  
Local Cohomology ◽  
Vanishing Theorems ◽  
Fundamental Properties ◽  
Normal Varieties

The foundations for this paper were developed in [5], “Seminormal rings and weakly normal varieties”, where the historical framework and fundamental properties of weakly normal varieties were presented in detail. Here we devote our attention to the study of the multicross singularity and the role of local cohomology in the theory of weakly normal varieties.

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 Intuitive representation of local cohomology groups

2020 ◽  
Vol 72 (2) ◽  
pp. 569-597
Author(s):  
Daichi KOMORI ◽  
Kohei UMETA
Keyword(s):  
Local Cohomology ◽  
Cohomology Groups
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