Sharp bounds on fake weighted projective spaces with canonical singularities

2021/05/20 by Gennadiy Averkov, Alexander Kasprzyk, Averkov, Gennadiy +5
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2105.09635

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.

Citations

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

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