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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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1435-5345
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Volume 2014, Issue 697

Issues

Reflexive differential forms on singular spaces. Geometry and cohomology

Daniel Greb
  • Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
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/ Stefan Kebekus
  • Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstraße 1, 79104 Freiburg im Breisgau, Germany
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/ Thomas Peternell
Published Online: 2013-01-09 | DOI: https://doi.org/10.1515/crelle-2012-0097

Abstract

Based on a recent extension theorem for reflexive differential forms, that is, regular differential forms defined on the smooth locus of a possibly singular variety, we study the geometry and cohomology of sheaves of reflexive differentials.

First, we generalise the extension theorem to holomorphic forms on locally algebraic complex spaces. We investigate the (non-)existence of reflexive pluri-differentials on singular rationally connected varieties, using a semistability analysis with respect to movable curve classes. The necessary foundational material concerning this stability notion is developed in an appendix to the paper. Moreover, we prove that Kodaira–Akizuki–Nakano vanishing for sheaves of reflexive differentials holds in certain extreme cases, and that it fails in general. Finally, topological and Hodge-theoretic properties of reflexive differentials are explored.

About the article

Received: 2012-02-27

Published Online: 2013-01-09

Published in Print: 2014-12-01


Funding Source: DFG

Award identifier / Grant number: “Classification of Algebraic Surfaces and Compact Complex Manifolds”

Funding Source: Baden-Württemberg-Stiftung

Award identifier / Grant number: “Eliteprogramm für Postdoktorandinnen und Postdoktoranden”


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2014, Issue 697, Pages 57–89, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2012-0097.

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Citing Articles

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[1]
Daniel Greb, Henri Guenancia, and Stefan Kebekus
Geometry & Topology, 2019, Volume 23, Number 4, Page 2051
[2]
Clemens Jörder
Mathematische Zeitschrift, 2014, Volume 278, Number 3-4, Page 893

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