Back to Algebraic Geometry Seminar: Fall 2012
Algebraic Geometry Seminar
Date: Tuesday, Oct 30, 2012
Time: 3:30PM - 4:30PM
Location: JTB 120
Zhixian Zhu
University of Michigan
Title |
Divisorial valuations via arcs in positive characteristic |
Abstract |
When X is a smooth complex variety, it was shown by Ein, Lazarsfeld and Mustata that there is a general correspondence between cylinders in the space of arcs of X and divisorial valuations of the function field of X. Via this correspondence, the codimension of the cylinders corresponds to the log discrepancy of the divisorial valuation. The use of log resolutions in their proof restricted the result to ground field of characteristic zero. In this talk, I’ll show this correspondence holds in arbitrary characteristic. In particular, we have Mustata’s formula, relating the log canonical threshold of a pair to the asymptotic behavior of the dimensions of the jet schemes, also available in positive characteristic. This has interesting applications, for example, to an inequality between log canonical threshold and F-pure threshold and to a version of inversion of adjunction in positivity characteristic. |
Algebraic Geometry