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arXiv · 2105.09635

Sharp bounds on fake weighted projective spaces with canonical singularities

Gennadiy Averkov·Alexander Kasprzyk·Martin Lehmann·Benjamin Nill
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Abstract

We give a sharp upper bound on the multiplicity of a fake weighted projective space with at worst canonical singularities. This is equivalent to giving a sharp upper bound on the index of the sublattice generated by the vertices of a lattice simplex containing only the origin as an interior lattice point. We also completely characterise when equality occurs and discuss related questions and conjectures.

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Gennadiy Averkov, Alexander Kasprzyk, Martin Lehmann, Benjamin Nill. 2021-05-20. Sharp bounds on fake weighted projective spaces with canonical singularities. https://arxiv.org/abs/2105.09635

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