Algebra & Number Theory

Comparing numerical dimensions

Brian Lehmann

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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.

Article information

Algebra Number Theory, Volume 7, Number 5 (2013), 1065-1100.

Received: 20 September 2011
Revised: 9 July 2012
Accepted: 3 August 2012
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14C20: Divisors, linear systems, invertible sheaves

divisor numerical dimension


Lehmann, Brian. Comparing numerical dimensions. Algebra Number Theory 7 (2013), no. 5, 1065--1100. doi:10.2140/ant.2013.7.1065.

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