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Recent results in several complex variables and complex geometry. (English. Russian original) Zbl 1458.32012

Proc. Steklov Inst. Math. 311, 245-260 (2020); translation from Tr. Mat. Inst. Steklova 311, 264-281 (2020).
Summary: We first recall the background and contents of our recent solutions of the optimal \(L^2\) extension problem and Demailly’s strong openness conjecture on multiplier ideal sheaves and related results, and then present some new related results in several complex variables and complex geometry.

MSC:

32D15 Continuation of analytic objects in several complex variables
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
32Q15 Kähler manifolds
32U05 Plurisubharmonic functions and generalizations
32W05 \(\overline\partial\) and \(\overline\partial\)-Neumann operators
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