AG seminar in SISSA on Tue March 28

[Jacopo Vittorio Scalise]

Dear all,
this is to announce the next weekly seminar in AG at SISSA.

4-4.30* pm, room 136, 28/03

*Before the actual talk starts, the speaker will present a 25-30 mins 
pre-talk aimed at grad students explaining some basic background in 
birational geometry and the minimal model program.

Speaker: Roberto Svaldi (SISSA/Univ. of Cambridge)

Title: A geometric characterization of toric varieties.

Abstract: Given a pair (X, D), where X is a proper variety and D a 
divisor with mild singularities, it is natural to ask how to bound the 
number of components of D or rather the sum of their (positive) 
coefficients. In general such bound does not exist. But when -(K_X+D) is 
positive, i.e. ample (or nef), then a conjecture of Shokurov says this 
bound should coincide with the sum of the dimension of X and its Picard 
number. When the bound is achieved, Shokurov conjectured that then X 
would be a toric variety and D a choice of toric invariant divisor. We 
prove a strengthened version of this conjecture and show that it 
suffices that the number of components of D is close enough to said sum 
for X to be a toric variety and D to be very close to a toric invariant 
divisor. Moreover, if time permits I will explain how to use the same 
kind of techniques to prove rationality of certain varieties. This is 
joint work with M. Brown, J. McKernan, R. Zong.


Everybody interested is welcome to attend.