|Speaker:||Shigefumi Mori (RIMS, Kyoto U)|
|Title:||On the classification of algebraic varieties|
|Date:||Mon, Dec 11, 2017, 15:30 - 16:30|
In my talk I will present my personal views on the area around my research; I have been studying algebraic varieties through rational curves on them.
I was first attracted to a very special problem called the Hartshorne Conjecture to characterize algebraic varieties which are "positively curved" in the strongest sense in Differential Geometry. After I managed to solve it, I was interested in a certain weaker notion of curvedness.
In terms of this meaure of posiively/negatively curvervedness, I realized that "an algebraic variety X is usually negatively curved, and there is a clear geometric reason if otherwise" (Theory of Extremal Rays). In the former case X is called a minimal model, while in the second there is a conjectural procedure called Minimal Model Program to transform X into a minimal model or a model with explicit global structure called Fano Fibering.
These has led to the biregular classification problem of certain algebraic varieties and furthermore to the general theory of higher dimensional birational classification. I will present them to a wider audience including mathematicians.