Title: Semi-continuity of log canonical threshold in singular central fiber case

Speaker: Yuchen Liu (Peking University)

Venue: Room 09 at Quan-Zhai (全斋), New location for BICMR, Peking University

Time: March 27, 2012, Tuesday, 14:00-16:00pm

Abstract: The log canonical threshold (or complex singularity exponent) of a holomorphic function is a real number related to the singularity of the zero set of the function. As Demailly-Kollar proved the semi-continuity of log canonical threshold in smooth case, the singular central fiber case is quite different. I will give a counterexample to show that the semi-continuity property doesn't hold in general in singular central fiber case, and I will impose some conditions to obtain the semi-continuity property in simple-normal-crossing case.