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Relative rounding in
toric and logarithmic geometry
Chikara Nakayama and Arthur Ogus |
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Geometry & Topology 14 (2010) 2189–2241
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Abstract |
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We show that the introduction of polar coordinates in toric geometry smoothes a wide class of equivariant mappings, rendering them locally trivial in the topological category. As a consequence, we show that the Betti realization of a smooth proper and exact mapping of log analytic spaces is a topological fibration, whose fibers are orientable manifolds (possibly with boundary). This turns out to be true even for certain noncoherent log structures, including some families familiar from mirror symmetry. The moment mapping plays a key role in our proof. |
Keywords
log geometry, smoothing, toric geometry, submersion,
duality, orientation, manifold with boundary
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Mathematical Subject Classification 2000
Primary: 14D06, 14M25, 14F45, 32S30
Secondary: 53D20, 14T05
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References |
Publication
Received: 11 March 2010
Revised: 23 August 2010
Accepted: 28 June 2010
Published: 28 October 2010
Proposed: Richard Thomas
Seconded: Jim Bryan, Frances Kirwan
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Authors |
| Chikara Nakayama | |
| Department of Mathematics Tokyo Institute of Technology Ookayama, Meguro-ku Tokyo 152-8551 Japan |
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| Arthur Ogus | |
| Department of Mathematics University of California Berkeley, CA 94720 USA |
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| http://www.math.berkeley.edu/~ogus | |
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