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Geometry & Topology Seminar

Title: Moduli space of Kahler-Einstein metrics of negative scalar curvature
Speaker: Jian Song (Rutgers University)
Date: 05 May 2021
Time: 9:00 pm
Venue: MS teams (team code hiq1jfr)

Let K(n, V) be the space of n-dimensional compact Kahler-Einstein manifolds with negative scalar curvature and volume bounded above by V. We prove that any sequence in K(n, V) converges in pointed Gromov-Hausdorff topology to a finite union of complete Kahler-Einstein metric spaces without loss of volume, which is biholomorphic to an algebraic semi-log canonical model with its non-log terminal locus removed. We further show that the Weil-Petersson metric extends uniquely to a Kahler current with continuous local potentials on the KSB compactification of the moduli space of canonically polarized manifolds. In particular, the Weil-Petersson volume of the KSB moduli space is finite.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 18 Sep 2021