MathematischeGesellschaft Non-archimedean Monge-Amp\`ere equations |  |
Speaker:Prof. Dr. Walter Gubler, Universität Regensburg
Location:Mathematisches Institut, Bunsenstr 3-5Sitzungszimmer, Bunsenstr. 3-5, 37073 GöttingenGras Geo Map
Organizer:Mathematisches Institut
Details:
Abstract:
We study non-archimedean volumes, a tool which allows us to control the asymptotic
growth of small sections of big powers of a metrized line bundle. We prove that the nonarchimedean
volume is differentiable at a continuous semipositive metric and that the derivative
is given by integration with respect to a Monge-Amp`ere measure. Such a differentiability formula
had been proposed by M. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies
an orthogonality property for non-archimedean plurisubharmonic functions which allows us to
drop an algebraicity assumption in a theorem of S. Boucksom, C. Favre and M. Jonsson about
the solution to the non-archimedean Monge-Amp`ere equation.
We study non-archimedean volumes, a tool which allows us to control the asymptotic
growth of small sections of big powers of a metrized line bundle. We prove that the nonarchimedean
volume is differentiable at a continuous semipositive metric and that the derivative
is given by integration with respect to a Monge-Amp`ere measure. Such a differentiability formula
had been proposed by M. Kontsevich and Y. Tschinkel. In residue characteristic zero, it implies
an orthogonality property for non-archimedean plurisubharmonic functions which allows us to
drop an algebraicity assumption in a theorem of S. Boucksom, C. Favre and M. Jonsson about
the solution to the non-archimedean Monge-Amp`ere equation.
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Type:Colloquium
Language:English
Category:Research
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