A geometric characterization of toric varieties

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• Roberto Svaldi (Cambridge)
• Wednesday 11 November 2015, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Caucher Birkar.

Given a pair (X, D), where X is a projective variety and D a divisor with mild singularities, it is natural to ask how to bound the number of components of D. In general such bound does not exist. But when -(K_X+D) is positive, i.e. ample (or nef), then a conjecture of Shokurov says this bound should coincide with the sum of the dimension of X and its Picard number. We prove the conjecture and show that if the bound is achieved, or the number of components is close enough to said sum, then X is a toric variety and D is close to being the toric invariant divisor. This is joint work with M. Brown, J. McKernan, R. Zong.

This talk is part of the Algebraic Geometry Seminar series.

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