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Today's seminar
Seminar information archive ～04/25｜Today's seminar 04/26 | Future seminars 04/27～
2024/04/26
Algebraic Geometry Seminar
14:00-15:30 Room #056 (Graduate School of Math. Sci. Bldg.)
Tatsuro Kawakami (Kyoto University)
Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)
Tatsuro Kawakami (Kyoto University)
Frobenius stable Grauert-Riemenschneider vanishing fails (日本語)
[ Abstract ]
We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.
We show that the Frobenius stable version of Grauert-Riemenschneider vanishing fails for a terminal 3-fold in characteristic 2. To prove this, we introduce the notion of $F_p$-rationality for singularities in positive characteristic, and prove that 3-dimensional klt singularities are $F_p$-rational. I will also talk about the vanishing of $F_p$-cohomologies of log Fano threefolds. This is joint work with Jefferson Baudin and Fabio Bernasconi.
Colloquium
15:30-16:30 Room #大講義室(auditorium) (Graduate School of Math. Sci. Bldg.)
Shouhei Honda (Graduate School of Mathematical Sciences, University of Tokyo)
Riemannian manifolds and their limit spaces (JAPANESE)
Shouhei Honda (Graduate School of Mathematical Sciences, University of Tokyo)
Riemannian manifolds and their limit spaces (JAPANESE)
[ Abstract ]
The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.
The Gromov-Hausdorff (GH) distance defines a distance on the set A of all isometry classes of Riemannian manifolds. Gromov established a precompactness result with respect to the GH distance, under assuming a lower bound on Ricci curvature. In particular we are able to discuss limit nonsmooth spaces of Riemannian manifolds with Ricci curvature bounded below. In this talk, we explain recent developments about this topic.
