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Alex Dimca (Nice)
Wednesday 09 November 2011, 14:15-15:15
Koszul complexes and pole order filtrations for projective hypersurfaces
- đ¤ Speaker: Alex Dimca (Nice)
- đ Date & Time: Wednesday 09 November 2011, 14:15 - 15:15
- đ Venue: MR13, CMS
Abstract
I’ll discuss the interplay between the cohomology of the Koszul complex of the partial derivatives of a homogeneous polynomial f and the pole order filtration P on the cohomology of the open set U=Pn-D, with D the hypersurface defined by f=0.
The relation is expressed by some spectral sequences, which may be used on one hand to determine the filtration P in many cases for curves and surfaces, and on the other hand to obtain information about the syzygies involving the partial derivatives of the polynomial f.
The case of a nodal hypersurface D is treated in terms of the defects of linear systems of hypersurfaces of various degrees passing through the nodes of D. When D is a nodal surface in P3, we show that F2H3(U) is not equal to P2H3(U) as soon as the degree of D is at least 4.
Series This talk is part of the Algebraic Geometry Seminar series.
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