Numerical and linear equivalence of divisors in birational geometry

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• Anne-Sophie Kaloghiros (Cambridge)
• Wednesday 25 May 2011, 14:15-15:15
• MR13, CMS.

If you have a question about this talk, please contact Burt Totaro.

Let X be a smooth projective variety and D a divisor on X. The MMP is concerned with determining a “good” model for D — that is, a variety X’ birational to X on which the image of D is a divisor with good positivity properties. In this talk, I will examine which part of this picture depends on the numerical equivalence class of D (topological properties) and which part depends on its linear equivalence class (algebro-geometric properties). I will introduce the numerical Zariski Decomposition of divisors. Under the hypothesis of finite generation, it can be used to recover Shokurov’s polytopes and to describe the relationship between different end products of the MMP on klt pairs (X, D) when D varies.

This talk is part of the Algebraic Geometry Seminar series.

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