## 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 |