Moduli Space of Hyperplane Arrangements

Location: 10th Floor Classroom Speaker Brooke Wei, University of California at Irvine Abstract We love compact moduli spaces! One method for compactifying moduli spaces is to consider moduli spaces of pairs of log general type (X,D) such that KX + D is ample, known as the KSBA (Kollár--Shepherd-Barron--Alexeev) compactification. In this talk, I will motivate the idea of KSBA stability by compactifying M0,n for n = 4 and 5, discuss general KSBA theory, and work out some stable replacements for the case of 5 lines on P2.