

International conference «Categorical and analytic invariants in Algebraic geometry 3»
September 12, 2016 11:00–12:00, Moscow






The Coherence of direct images of relative De Rham complex
K. Saito^{} ^{} Kavli Institute for the Physics and Mathematics of the Universe

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Abstract:
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 wellknown since the entries of Hodge to De Rham spectral sequence is already coherent. Therefore, our interest is the case for a nonproper (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 KoszulDe Rham algebra, which seems to be of interest by itself.
Language: English

