Séminaires : Séminaire de géométrie algébrique

La page officielle du Séminaire

Le jeudi à 14h.
septembre-décembre Sophie-Germain, janvier-mars ENS, avril-juin Jussieu

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On a Fano variety, the Yau-Tian-Donaldson correspondence connects the existence of Kähler-Einstein metrics to an algebro-geometric notion called K-stability. In the last decade, the latter has proved to be very valuable in Algebraic Geometry: for instance, it is used for the construction of moduli spaces. In the first part of the talk, partly motivated by the study of Kähler-Einstein metrics with prescribed singularities, a new relative K-stability notion will be introduced for a fixed smooth Fano variety. A particular focus will be given to motivations and intuitions, making a comparison with the log K- stability/log Kähler-Einstein metrics. The relative K-stability and the Kähler-Einstein metrics with prescribed singularities will then be related to each other through a Yau- Tian-Donaldson correspondence, which will be the core of the talk. An important role will be played by algebro-geometric valuative criteria, which will be also used to link the relative K-stability to the genuine K-stability.