3.30 pm, Lecture Hall 6
Weak-Boundedness of Fano 3-folds in Characteristic p>5
University of California, USA.
Classifying all varieties is one of the main goals of algebraic geometry. One way to classify varieties is finding their moduli spaces. The first problem in constructing a moduli space is proving the boundedness of the moduli functor. The boundedness of Fano varieties (A variety X is called Fano if -K_X is ample) is known as the Borisov-Alexeev-Borisov or the BAB Conjecture. For Fano surface (i.e., singular del Pezzo surfaces) this conjecture was known for nearly 25 years now (since 1994), due to Alexeev. Then in 2016 in a series of two breakthrough papers, Birkar proved that the BAB Conjecture holds in full generality in all dimensions over a filed of Characteristic 0. This led to his Fields Medal this year (2018). Despite this major progress in char 0, very little is known about the BAB conjecture in Positive Characteristic in dimension 3 and higher. In this talk I will show that a weak version of the BAB conjecture known as the `Weak-BAB Conjecture' holds for Fano 3-folds in char p>5.