Introduction to the MMP and classification of Fano manifolds

“Doc in Progress” is pleased to introduce you to:

• Saverio Andrea Secci - PhD in Mathematics - University of Torino

One of the main goals in many areas of Mathematics is to classify the studied objects up to some equivalence relation. In the case of Algebraic Geometry, this often results in the classification of projective varieties up to isomorphism. However, there are many properties of a projective (complex) variety that are invariant under birational transformations.
Thus we ask: given a projective variety X, is there a projective variety Y birationally equivalent to X, which is ’the simplest’ in some sense? If such a Y exists, it is called a minimal model. After an introduction to Mori’s Theory, and the Minimal Model Program (MMP), we will see some of its applications to the classification of Fano manifolds.