Bounds on fake weighted projective space

By Alexander M. Kasprzyk. 2008

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A fake weighted projective space X is a Q-factorial toric variety with Picard number one. As with weighted projective space, X comes equipped with a set of weights (\lambda_0,...,\lambda_n). We see how the singularities of P(\lambda_0,...,\lambda_n) influence the singularities of X, and how the weights bound the number of possible fake weighted projective spaces for a fixed dimension. Finally, we present an upper bound on the ratios \lambda_j/\sum\lambda_i if we wish X to have only terminal (or canonical) singularities.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b377b2374782c30300f9826def9d5e7aa71c2410