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25/04/2024 | 14h00 (1016) Bat. S. Germain | Tiago Duarte-Guerreiro, Examples of Mori Dream spaces of Picard rank 2 and their birational geometry |
| | L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion Abstract: Let X be an n-dimensional smooth projective Fano hypersurface, where n is at least 3. Suppose X contains Z, a k-dimensional smooth projective hypersurface in P^{k+1}, where k is at least 1. We give a constructive proof that Y - the blowup of X along Z - is a Mori dream space. In particular, we describe its Mori chamber decomposition and the associated birational models of Y. This is joint work with L. Campo and E. Paemurru. |
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02/05/2024 | 14h00 (1016) Bat. S. Germain | Matthew Baker, Band schemes and moduli spaces of matroids |
| | Abstract: We introduce a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Among other things, band schemes provide a new viewpoint on tropical geometry and Berkovich analytifications, and they enable a partial explanation for phenomena observed by Jacques Tits concerning algebraic groups over the "field of one element". Band schemes also furnish a natural algebro-geometric setting for studying matroid theory; in particular, they allow us to construct a moduli space of matroids, and they provide new tools for studying realization spaces of matroids. If time permits, we will discuss applications to a generalization of Laurent Lafforgue's theorem on realization spaces of rigid matroids. This is joint work with Oliver Lorscheid and Tong Jin. |
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16/05/2024 | 14h00 (1016) Bat. S. Germain | Yueqiao Wu, K-semistability of log Fano cone singularities |
| | L'exposé sera aussi diffusé par ZOOM:870 3083 2332, demander le mot de passe à Olivier Benoist, Olivier Debarre ou Frederic Han, ou inscrivez vous sur la liste de diffusion Abstract: K-stability of log Fano cone singularities was introduced by Collins-Sz\’ekelyhidi to serve as a local analog of K-stability of Fano varieties. In the Fano case, the result of Li-Xu states that to test K-stability, it suffices to test the so-called special test configurations. In this talk, I will talk about a local version of this result for log Fano cones. Our method relies on a non-Archimedean characterization of local K-stability. |
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