# Séminaires : Séminaire de géométrie algébrique

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Email des responsables : frederic.han@imj-prg.fr
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#### Le jeudi à 14h. septembre-décembre Sophie-Germain, janvier-mars ENS, avril-juin Jussieu

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 Orateur(s) Masafumi Hattori - , Titre On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves Date 02/02/2023 Horaire 14:00 à 15:00 Diffusion Résume l'exposé sera aussi diffusé par ZOOM: https://u-paris.zoom.us/j/87030832332 , demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion
Abstract: Algebro-geometers have made a remarkable progress in the study of K-stability of log Fano pairs and constructed their K-moduli in ten years. On the other hand, K-moduli is also constructed for the K-ample case (so-called KSBA moduli) and the Calabi-Yau case (but the moduli is not compact in this case). Nevertheless, moduli spaces parametrizing more general klt polarized K-stable varieties have not been constructed yet. In this talk, we consider adiabatic’' K-stability of Calabi-Yau fibrations over curves (e.g., good minimal models with $\kappa(X)=1$, rational elliptic surfaces, etc.) and try constructing adiabatic’' K-moduli. First, we treat boundedness for such fibrations. Here, we only use a certain assumption on the volume of a general fiber. Furthermore, we construct moduli spaces of polarized uniformly adiabatically K-stable klt-trivial fibrations over curves by applying this boundedness and the criterion for uniform adiabatic K-stability. This talk is based on a joint work with Kenta Hashizume.| Salle ENS salle W Adresse ENS
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