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Some aspects of Hodge theory on non-complete algebraic manifolds

Title data

Bauer, Ingrid ; Kosarew, Siegmund:
Some aspects of Hodge theory on non-complete algebraic manifolds.
In: Noguchi, Junjiro ; Ohsawa, Takeo (ed.): Prospects in complex geometry : proceedings. - Berlin : Springer , 1991 . - pp. 281-316 . - (Lecture Notes in Mathematics ; 1468 )
ISBN 978-3-540-47370-1
DOI: https://doi.org/10.1007/BFb0086198

Review:

Abstract in another language

Let U be a smooth algebraic variety. The authors continue their study of the Dolbeault and de Rham cohomology groups on U which admits a compactification X of a certain type. The situation is divided into two cases, which correspond to the notion of concavity and convexity in complex analytic geometry. The first one is "Y:=X−U is of `high' codimension in X'' and the other is "Y is a divisor, X is smooth and the normal bundle NY/X satisfies a suitable positivity condition''. Their results contain finiteness theorems, Lefschetz type theorems, Hodge theory, and vanishing theorems of Akizuki-Nakano type. An interesting counterexample is also given. The paper is written in a survey style.

Further data

Item Type: Article in a book
Refereed: Yes
Subject classification: Mathematics Subject Classification Code: 32J25 (14C30 14F17 32C35 32L20)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Algebraic Geometry > Professor Algebraic Geometry - Univ.-Prof. Dr. Ingrid Bauer
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professor Algebraic Geometry
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 14 Jun 2021 09:11
Last Modified: 14 Jun 2021 11:03
URI: https://eref.uni-bayreuth.de/id/eprint/65855