Notions of numerical Iitaka dimension do not coincide
Author:
John Lesieutre
Journal:
J. Algebraic Geom.
DOI:
https://doi.org/10.1090/jag/763
Published electronically:
February 2, 2021
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Abstract | References | Additional Information
Abstract: Let be a smooth projective variety. The Iitaka dimension of a divisor
is an important invariant, but it does not only depend on the numerical class of
. However, there are several definitions of ``numerical Iitaka dimension'', depending only on the numerical class. In this note, we show that there exists a pseuodoeffective
-divisor for which these invariants take different values. The key is the construction of an example of a pseudoeffective
-divisor
for which
is bounded above and below by multiples of
for any sufficiently ample
.
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Additional Information
John Lesieutre
Affiliation:
The Pennsylvania State University, 204 McAllister Building, University Park, Pennsylvania 16801
Email:
jdl@psu.edu
DOI:
https://doi.org/10.1090/jag/763
Received by editor(s):
June 5, 2019
Received by editor(s) in revised form:
January 16, 2020
Published electronically:
February 2, 2021
Additional Notes:
This work was supported by NSF Grant DMS-1700898/DMS-1912476.