| 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 <a href="https://listes.services.cnrs.fr/wws/subscribe/sem-ga.paris">liste de diffusion</a><br>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.| |
