Numerical analogues of the Kodaira dimension and the Abundance Conjecture

Eckl, Thomas (2016) Numerical analogues of the Kodaira dimension and the Abundance Conjecture. MANUSCRIPTA MATHEMATICA, 150 (3-4). pp. 337-356.

Text NumericalDimensionsAbundance-arXiv.pdf - Unspecified Download (456kB)

Abstract

We add further notions to Lehmann’s list of numerical analogues to the Kodaira dimension of pseudo-effective divisors on smooth complex projective varieties, and show new relations between them. Then we use these notions and relations to fill in a gap in Lehmann’s arguments, thus proving that most of these notions are equal. Finally, we show that the Abundance Conjecture, as formulated in the context of the Minimal Model Program, and the Generalized Abundance Conjecture using these numerical analogues to the Kodaira dimension, are equivalent for non-uniruled complex projective varieties.

Item Type:	Article
Depositing User:	Symplectic Admin
Date Deposited:	28 Sep 2015 08:42
Last Modified:	16 Dec 2022 15:27
DOI:	10.1007/s00229-015-0815-x
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/2028360

Available Versions of this Item

• Numerical analogues of the Kodaira dimension and the Abundance Conjecture. (deposited 28 Sep 2015 08:42) [Currently Displayed]