Toric manifolds over 3-polytopes

Anton Ayzenberg

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arXiv · 1607.03377

Toric manifolds over 3-polytopes

Anton Ayzenberg

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Abstract

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.

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BibTeX RIS

Anton Ayzenberg. 2016-07-12. Toric manifolds over 3-polytopes. https://arxiv.org/abs/1607.03377

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