BooksecrCollected Volumepp. 319–334

Sharp bounds on fake weighted projective spaces with canonical singularities

  • Gennadiy Averkov

    Brandenburg University of Technology Cottbus-Senftenberg, Germany
    ORCID

  • Alexander M. Kasprzyk

    University of Warwick, Coventry, UK
    ORCID

  • Martin Lehmann

    Otto-von-Guericke University Magdeburg, Germany

  • Benjamin Nill

    Otto-von-Guericke University Magdeburg, Germany
    ORCID
Sharp bounds on fake weighted projective spaces with canonical singularities cover
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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.