ICTP Algebraic Geometry Seminars - Wednesday, 12 October, at 15:30 (Diletta Martinelli)/hybrid seminar

[ICTP/math - Di Giovannantonio Margherita]

ICTP ALGEBRAIC GEOMETRY SEMINARS 2022

Wednesday, 12 October, at 15:30

Hybrid seminar

Venue: for in-person attendees (Leonardo da Vinci, Luigi Stasi seminar 
room).

For virtual attendees:
https://zoom.us/meeting/register/tJEodeyspjooE9RLusdnk-qwB3tk0VcT8kuM
After registering, you will receive a confirmation email containing 
information about joining the meeting.




Kindly note that this seminar is divided in two parts of roughly 45 
minutes each. The first part is for more general audience, while the 
second part is more specialized.



Speaker: Diletta Martinelli (University of Amsterdam)


Part 1: Introduction to birational geometry and the Minimal Model Program
The Minimal Model Program is an important framework in the 
classification of projective varieties up to birational equivalence. In 
the talk, I plan to give an accessible introduction to the subject and 
describe some recent advances in the theory.


Part 2: Gale duality, blowups and moduli spaces
The Gale correspondence provides a duality between sets of n points in 
projective spaces P^s and P^r when n=r+s+2. For small values of s, this 
duality has a remarkable geometric manifestation: the blowup of P^r at n 
points can be realized as a moduli space of vector bundles on the blowup 
of P^s at the Gale dual points. We explore this realization to describe 
the birational geometry of blowups of projective spaces at points in 
very general position. We will focus in particular on the cases where 
the blowup fails to be a Mori Dream Space, reporting on a joint work 
with Carolina Araujo, Ana-Maria Castravet and Inder Kaur.


https://indico.ictp.it/event/10077/