Valuative multiplier ideals

Zhengyu Hu

Vol. 270 (2014), No. 1, 95–128

DOI: 10.2140/pjm.2014.270.95

Abstract

The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general scheme. We then define the multiplier ideals of these functions and prove some basic results about them, such as subadditivity property, the approximation theorem. We also treat some applications in complex algebraic geometry.

Keywords

multiplier ideals, valuations

Mathematical Subject Classification 2010

Primary: 14F18

Secondary: 12J20

Milestones

Received: 1 February 2012

Revised: 7 May 2014

Accepted: 13 May 2014

Published: 2 August 2014