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Description

The Iitaka dimension of a line bundle D on a projective variety X is the dimension of the image of the rational map given by |mD| for large and divisible m. The Iitaka dimension is not a numerical invariant of D, and there are several approaches to constructing a "numerical dimension", which should be an analogous invariant depending only on the numerical class of D. I will discuss some divisors of dynamical origin that have unexpected behavior with respect to these invariants.