A twisted ∂¯f-Neumann problem and Toeplitz n-tuples from singularity theory

A twisted ∂ ¯ f -Neumann problem associated to a singularity ( O n , f ) is established. By relating it to the Koszul complex for Toeplitz n -tuples ( f 1 , … , f n ) , where f i = ∂ f ∂ z i , on Bergman space B 0 ( D ) , this ∂ ¯ f -Neumann problem is solved. Moreover, the cohomology of the L 2 -ho...

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Vydáno v:Manuscripta mathematica Ročník 156; číslo 1-2; s. 63 - 80
Hlavní autoři: Wen, Hao, Fan, Huijun
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2018
Springer Nature B.V
Témata:
Algebraic Geometry
Calculus of Variations and Optimal Control; Optimization
Geometry
Lie Groups
Mathematics
Mathematics and Statistics
Neumann problem
Number Theory
Topological Groups
58K99
32W99
ISSN:0025-2611, 1432-1785
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Shrnutí:A twisted ∂ ¯ f -Neumann problem associated to a singularity ( O n , f ) is established. By relating it to the Koszul complex for Toeplitz n -tuples ( f 1 , … , f n ) , where f i = ∂ f ∂ z i , on Bergman space B 0 ( D ) , this ∂ ¯ f -Neumann problem is solved. Moreover, the cohomology of the L 2 -holomorphic Koszul complex ( B ∗ ( D ) , ∂ f ∧ ) can be computed explicitly.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-2611
1432-1785
DOI:10.1007/s00229-017-0953-4