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Creators/Authors contains: "LESIEUTRE, JOHN"

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  1. (, Journal of Algebraic Geometry)
    null (Ed.)
    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 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,mD_+ + A)$ is bounded above and below by multiples of m^{3/2} for any sufficiently ample A. 
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  2. (, Journal of Modern Dynamics)
    null (Ed.)
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  3. ; ; ; ; (, ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE)
    null (Ed.)
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  4. ; (, International Mathematics Research Notices)
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  5. ; (, Ergodic Theory and Dynamical Systems)
    Let be a dominant rational self-map of a smooth projective variety defined over $$\overline{\mathbb{Q}}$$ . For each point $$P\in X(\overline{\mathbb{Q}})$$ whose forward $$f$$ -orbit is well defined, Silverman introduced the arithmetic degree $$\unicode[STIX]{x1D6FC}_{f}(P)$$ , which measures the growth rate of the heights of the points $$f^{n}(P)$$ . Kawaguchi and Silverman conjectured that $$\unicode[STIX]{x1D6FC}_{f}(P)$$ is well defined and that, as $$P$$ varies, the set of values obtained by $$\unicode[STIX]{x1D6FC}_{f}(P)$$ is finite. Based on constructions by Bedford and Kim and by McMullen, we give a counterexample to this conjecture when $$X=\mathbb{P}^{4}$$ . 
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  6. (, Inventiones mathematicae)
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