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A Calabi-Yau Theorem for Degenerations of Compact Kähler ManifoldsTo understand a compact Kähler manifold X, it is often helpful to study its degenerations. The idea of non-Archimedean (n-A) Kähler geometry is to think of such degenerations as (possibly weak) Kähler potentials on an associated n-A space. The n-A Monge-Ampère measure of a degeneration is then supposed to encode how the volume of X distributes as X degenerates. In this talk I will discuss a Calabi-Yau theorem in this setting, first proved in the algebraic case by Sébastien Boucksom and Mattias Jonsson (building on earlier work of Sébastien Boucksom, Charles Favre and Mattias Jonsson), and subsequently proved in the general Kähler case by Pietro Mesquita-Piccione and myself. The proof in the Kähler case relies on properties of big cohomology classes, and is related to the transcendental Morse inequality conjecture of Sébastien Boucksom, Jean-Pierre Demailly, Mihai Păun and Thomas Peternell.Uploaded 06-10-26 Learn more about your ad choices. Visit megaphone.fm/adchoices
