Relative rounding in toric and logarithmic geometry

Nakayama, Chikara¹ ; Ogus, Arthur²

¹ Department of Mathematics, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8551, Japan
² Department of Mathematics, University of California, Berkeley, CA 94720, USA

Geometry & topology, Tome 14 (2010) no. 4, pp. 2189-2241.

Résumé

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.

Détail

DOI : 10.2140/gt.2010.14.2189

Keywords: log geometry, smoothing, toric geometry, submersion, duality, orientation, manifold with boundary

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