Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 pseuodoeffective $\mathbb R$-divisor for which these invariants
take different values. The key is the construction of an example of a
pseudoeffective $\mathbb R$-divisor $D_+$ for which $h^0(X,\lfloor m D_+
\rfloor+A)$ is bounded above and below by multiples of $m^{3/2}$ for any
sufficiently ample $A$.

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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ