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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 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.

Language: English

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