Toric manifolds over 3-polytopes

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1. Verfasser: Ayzenberg, Anton
Format: Preprint
Veröffentlicht: 2016
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_version_ 1866908820766195712
author Ayzenberg, Anton
author_facet Ayzenberg, Anton
contents In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not correspond to any smooth projective toric variety. We restate the proof of the second claim which does not refer to complicated algebro-geometrical technique. If follows from these results that any fullerene supports quasitoric manifolds but does not support smooth projective toric varieties.
format Preprint
id arxiv_https___arxiv_org_abs_1607_03377
institution arXiv
publishDate 2016
record_format arxiv
spellingShingle Toric manifolds over 3-polytopes
Ayzenberg, Anton
Algebraic Topology
Algebraic Geometry
Combinatorics
Primary 52B10, 14M25, 57N16, Secondary 05E40, 05E45, 52B20, 14C25, 53D05, 57N65, 57R19
In this note we gather and review some facts about existence of toric spaces over 3-dimensional simple polytopes. First, over every combinatorial 3-polytope there exists a quasitoric manifold. Second, there exist combinatorial 3-polytopes, that do not correspond to any smooth projective toric variety. We restate the proof of the second claim which does not refer to complicated algebro-geometrical technique. If follows from these results that any fullerene supports quasitoric manifolds but does not support smooth projective toric varieties.
title Toric manifolds over 3-polytopes
topic Algebraic Topology
Algebraic Geometry
Combinatorics
Primary 52B10, 14M25, 57N16, Secondary 05E40, 05E45, 52B20, 14C25, 53D05, 57N65, 57R19
url https://arxiv.org/abs/1607.03377