Mathematical Colloquium: The geometry of Fano varieties

Cinzia Casagrande
Universita’ di Torino
Friday, June 16, 2017 - 10:45 to 11:45

Given a smooth complex projective variety X, many geometrical properties of X depend on its canonical line bundle, the determinant of the cotangent bundle of X. Varieties with positive/trivial/negative canonical line bundle play a distinguished role in the birational classification of complex projective varieties, in the framework of the Minimal Model Program. In particular, X is a Fano variety if its canonical line bundle is negative (more precisely, its dual is ample); this yields many nice properties and a rich geometry. We will review the role of Fano varieties in the framework of the Minimal Model Program, and then explain some of their properties.

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