Back to Departmental Colloquium: Spring 2011
Departmental Colloquium
Date: Thursday, Jan 27, 2011
Time: 4:15PM
Location: JWB 335
Chenyang Xu
Massachusetts Institute of Technology
Title |
Boundedness of algebraic varieties |
Abstract |
In 19 century, Hurwitz proved that for any compact Riemann surfaces of genus g>1, the order of its automorphism group is bounded by 84(g-1). We prove a natural generalization of this result to all dimensions. In fact, this generalization itself is a special case of a conjecture on volumes of algebraic varieties due to Alexeev-Koll'ar. Our work verifies this conjecture. If time permits, I will talk about various other applications to justify that our results play important roles in the study of birational geometry and related fields. This is a joint work with Christopher Hacon and James McKernan. |
Algebraic Geometry
Geometry and Topology