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June, 2000 Compact Self-Dual Manifolds with Torus Actions
Akira Fujiki
J. Differential Geom. 55(2): 229-324 (June, 2000). DOI: 10.4310/jdg/1090340879

Abstract

We show that a compact self-dual four-manifold with a smooth action of a two-torus and with non-zero Euler characterestic is necessarily diffeomorphic to a connected sum of copies of complex projective planes, and furthermore the self-dual structure is isomorphic to one of those constructed by Joyce in [11]. This settles a conjecture of Joyce [11] affirmatively. Our method of proof is to show, by complex geometric techniques, that the associated twistor space, which is a compact complex threefold with the induced holomorphic action of algebraic two-torus, has a very special structure and is indeed determined by a certain invariant which is eventually identified with the invariant associated with the Joyce's construction of his self-dual manifolds.

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Akira Fujiki. "Compact Self-Dual Manifolds with Torus Actions." J. Differential Geom. 55 (2) 229 - 324, June, 2000. https://doi.org/10.4310/jdg/1090340879

Information

Published: June, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1032.57036
MathSciNet: MR1847312
Digital Object Identifier: 10.4310/jdg/1090340879

Rights: Copyright © 2000 Lehigh University

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Vol.55 • No. 2 • June, 2000
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