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arXiv · 1611.00735

On the mean Euler characteristic of Gorenstein toric contact manifolds

Miguel Abreu·Leonardo Macarini
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Abstract

We prove that the mean Euler characteristic of a Gorenstein toric contact manifold, i.e. a good toric contact manifold with zero first Chern class, is equal to half the normalized volume of the corresponding toric diagram and give some applications. A particularly interesting one, obtained using a result of Batyrev and Dais, is the following: twice the mean Euler characteristic of a Gorenstein toric contact manifold is equal to the Euler characteristic of any crepant toric symplectic filling, i.e. any toric symplectic filling with zero first Chern class.

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Miguel Abreu, Leonardo Macarini. 2016-11-02. On the mean Euler characteristic of Gorenstein toric contact manifolds. https://arxiv.org/abs/1611.00735

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