Bounds on Fake Weighted Projective Space

Details Bounds on Fake Weighted Projective Space Bounds on Fake Weighted Projective Space

2008-05-07

arxiv.org/abs/0805.1008v2

Kodai Mathematical Journal, 32 (2009), 197-208

Mathematics

Algebraic Geometry

12 pages

Scientific paper

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.

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