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University of Cambridge > Talks.cam > Algebraic Geometry Seminar > Koszul complexes and pole order filtrations for projective hypersurfaces

## Koszul complexes and pole order filtrations for projective hypersurfacesAdd to your list(s) Download to your calendar using vCal - Alex Dimca (Nice)
- Wednesday 09 November 2011, 14:15-15:15
- MR13, CMS.
If you have a question about this talk, please contact Burt Totaro. 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=P 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 F This talk is part of the Algebraic Geometry Seminar series. ## This talk is included in these lists:- Algebraic Geometry Seminar
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