Notions of numerical Iitaka dimension do not coincide
Let X be a smooth projective variety. The Iitaka dimension of a divisor D is an important invariant, but it does not only depend on the numerical class of D. However, there are several definitions of “numerical Iitaka dimension”, depending only on the numerical class. In this note, we show that there exists a pseudoeffective R-divisor for which these invariants take different values. The key is the construction of an example of a pseudoeffective R-divisor D+ for which h 0 (X, bmD+c + A) is bounded above and below by multiples of m3/2 for any sufficiently ample A.
First published in Journal of Algebraic Geometry on 2021-02-02, published by the American Mathematical Society. © 2021 American Mathematical Society.
|Work Title||Notions of numerical Iitaka dimension do not coincide|
|License||CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)|
|Publication Date||February 2, 2021|
|Publisher Identifier (DOI)||
|Deposited||May 23, 2022|
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