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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Relative rounding in toric and logarithmic geometry

Chikara Nakayama and Arthur Ogus

Geometry & Topology 14 (2010) 2189–2241
Abstract

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
Mathematical Subject Classification 2000
Primary: 14D06, 14M25, 14F45, 32S30
Secondary: 53D20, 14T05
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
Authors
Chikara Nakayama
Department of Mathematics
Tokyo Institute of Technology
Ookayama, Meguro-ku
Tokyo 152-8551
Japan
Arthur Ogus
Department of Mathematics
University of California
Berkeley, CA 94720
USA
http://www.math.berkeley.edu/~ogus