Abstract:

Recently, the bigness of the tangent bundle of Fano threefolds with Picard number 1 were determined by Höring, Liu, and Shao by using the total dual VMRT. In this talk, I will explain the theory of the total dual VMRT and its application to study the bigness of the tangent bundle of a Fano threefold or the blow-up of nondegenerate smooth curve in  . Through an explicit description of irreducible effective divisors in constructed from the total dual VMRT of the family of lines and conics, we determine successfully the bigness of the tangent bundle of whole 36 deformation types of Fano threefolds with Picard number 2. This is a joint work with Hosung Kim and Jeong-Seop Kim.