Mutations of Fake Weighted Projective Spaces

Bounds on Fake Weighted Projective Space

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 (λ0, . . . , λn). We see how the singularities of P(λ0, . . . , λn) 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 uppe...

Arithmetic Fake Projective Spaces and Arithmetic Fake Grassmannians

On the Cohomological Crepant Resolution Conjecture for Weighted Projective Spaces

We investigate the Cohomological Crepant Resolution Conjecture for reduced Gorenstein weighted projective spaces. Using toric methods, we prove this conjecture in some new cases. As an intermediate step, we show that weighted projective spaces are toric Deligne-Mumford stacks. We also describe a combinatorial model for the orbifold cohomology of weighted projective spaces.

The Chen-ruan Orbifold Cohomology of Weighted Projective Spaces

Chen and Ruan [6] defined a very interesting cohomology theoryChen-Ruan orbifold cohomology. The primary objective of this paper is to compute the Chen-Ruan orbifold cohomology of the weighted projective spaces, one of the most important space used in physics. The classical tools (orbifold cohomology defined by Chen and Ruan, toric varieties, the localization technique) which have been proved t...

Biquaternions Lie Algebra and Complex-Projective Spaces

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