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Singularities of plurisubharmonic functions, Monge-Ampère operators and holomorphic Morse inequalities
【2012.12.11/13/18 10:00am,S712】

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 2012-12-06  

  Colloquia & Seminars 

  Speaker

  Prof. J.P. Demailly,Fourier Institute, Univ. og Grenoble

  Title

  Singularities of plurisubharmonic functions, Monge-Ampère operators and holomorphic Morse inequalities

  Time

  2012.12.11/13/18 10:00am

  Venue

  S712

  Abstract

      Every closed positive (1,1)-current can be approximated by currents with analytic singularities - this result uses in an essential way the Ohsawa-Takegoshi L2 extension theorem in its proof, and can be seen as a generalization of Zariski decomposition in algebraic geometry. We use these techniques to derive several consequences in algebraic and analytic geometry :
- an optimal lower bound for the log canonical threshold of isolated plurisubharmonic singularities (joint work with Pham Hoang Hiep)
- results on asymptotic cohomology, in relation with holomorphic Morse inequalities and an inverse Andreotti-Grauert theorem.
- regularity theorems for solutions of Monge-Ampère equations.

  Affiliation

     

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