Dear friends of FRAGMENT,
this week we are very happy to have Giovanni Inchiostro visit us from University of Washington. Seminar lunch at 12noon for the interested (grad students subsidized).
See you soon!

Consider a quasi-compact moduli space M of pairs (X,D) consisting of a variety X and a divisor D on X. If M is not proper, it is reasonable to find a compactification of it. Assume furthermore that there are two rational numbers 0<b<a<1 such that, for every pair (X,D) corresponding to a point in M, the pairs (X,aD) and (X,bD) are klt, and the Q-divisors K_X+aD and K_X+bD are ample. Using Kollár’s formalism of stable pairs, one can construct two different compactifications of M (M_a and M_b), corresponding to a and b. One may wonder how to relate these two compactifications. The main result is that, up to replacing M_a and M_b with their normalizations, there are birational morphisms M_a \to M_b. This project is inspired by Hassett’s work on weighted stable curves, and is joint with Kenny Ascher, Dori Bejleri and Zsolt Patakfalvi.