English

Comparing numerical dimensions

Algebraic Geometry 2015-08-21 v5

Abstract

The numerical dimension is a numerical measure of the positivity of a pseudo-effective divisor LL. There are several proposed definitions of the numerical dimension due to Nakayama (2004) and Boucksom et al. (2004). We prove the equality of these notions and give several additional characterizations. We also prove some new properties of the numerical dimension.

Keywords

Cite

@article{arxiv.1103.0440,
  title  = {Comparing numerical dimensions},
  author = {Brian Lehmann},
  journal= {arXiv preprint arXiv:1103.0440},
  year   = {2015}
}

Comments

35 pages; update 2015: there is an important mistake in the proof of Proposition 5.3 which affects the main theorem. Please see Eckl's paper (http://arxiv.org/abs/1505.01262) for details

R2 v1 2026-06-21T17:34:14.503Z