Displaying similar documents to “Harmonic metrics and connections with irregular singularities”

Local and canonical heights of subvarieties

Walter Gubler (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Classical results of Weil, Néron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the * -product of Gillet-Soulé developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using...

On Deligne-Malgrange lattices, resolution of turning points and harmonic bundles

Takuro Mochizuki (2009)

Annales de l’institut Fourier

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In this short survey, we would like to overview the recent development of the study on Deligne-Malgrange lattices and resolution of turning points for algebraic meromorphic flat bundles. We also explain their relation with wild harmonic bundles. The author hopes that it would be helpful for access to his work on wild harmonic bundles.

On the singularities of the inverse to a meromorphic function of finite order.

Walter Bergweiler, Alexander Eremenko (1995)

Revista Matemática Iberoamericana

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Our main result implies the following theorem: Let f be a transcendental meromorphic function in the complex plane. If f has finite order ρ, then every asymptotic value of f, except at most 2ρ of them, is a limit point of critical values of f. We give several applications of this theorem. For example we prove that if f is a transcendental meromorphic function then f'fn with n ≥ 1 takes every finite non-zero value infinitely often. This proves a conjecture...