Vol. 7, No. 5, 2013

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ISSN: 1944-7833 (e-only)
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Comparing numerical dimensions

Brian Lehmann

Vol. 7 (2013), No. 5, 1065–1100
Abstract

The numerical dimension is a numerical measure of the positivity of a pseudoeffective divisor L. There are several proposed definitions of the numerical dimension due to Nakayama and Boucksom et al. We prove the equality of these notions and give several additional characterizations. We also prove some new properties of the numerical dimension.

Keywords
divisor, numerical dimension
Mathematical Subject Classification 2010
Primary: 14C20
Milestones
Received: 20 September 2011
Revised: 9 July 2012
Accepted: 3 August 2012
Published: 6 September 2013
Authors
Brian Lehmann
Department of Mathematics
Rice University
6100 Main Street
Houston, TX
77005
United States