Speaker: Omprokash Das (UCLA.)

Title: On the abundance problem for 3-folds in characteristic p>5.

 

Abstract: Let X be a smooth variety such that the canonical divisor K_X is nef. Then the Abundance Conjecture claims that | mK_X | is a base-point free linear system for some sufficiently large positive integer m. In characteristic 0 this conjecture is known to be true in full generality up to dimension 3, however in characteristic p>0 until very recently it was only known up to dimension 2. In this talk I will discuss the recent progress on the conjecture in dimension 3 and characteristic p>5. I will also explain and compare the unique difficulties and challenges which appear in proving the conjecture in positive characteristic in contrast to the characteristic 0 case.