Видеотека: K. Saito, The Coherence of direct images of relative De Rham complex

ВИДЕОТЕКА


Международная конференция «Categorical and analytic invariants in Algebraic geometry 3» 12 сентября 2016 г. 11:00, г. Москва, НИУ «Высшая школа экономики»

The Coherence of direct images of relative De Rham complex K. Saito Kavli Institute for the Physics and Mathematics of the Universe
Аннотация: We show the coherence of direct images of relative De Rham complex for holomorphic map $\Phi$ with a suitable boundary condition. When the map $\Phi$ is proper, the result is classical and is well-known since the entries of Hodge to De Rham spectral sequence is already coherent. Therefore, our interest is the case for a non-proper (open) map which possesses critical points (not necessarily isolated). Then, the result implies certain finitely generatedness of vanishing cycles for the critical points. For the proof, we develop a new concept of Koszul-De Rham algebra, which seems to be of interest by itself. Язык доклада: английский