BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Koszul complexes and pole order filtrations for projective hypersu
 rfaces - Alex Dimca (Nice)
DTSTART:20111109T141500Z
DTEND:20111109T151500Z
UID:TALK33069@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:I'll discuss the interplay between the cohomology of the\nKosz
 ul complex\nof the partial derivatives of a homogeneous polynomial f and t
 he\npole order filtration P\non the cohomology of the open set U=P^n-D\,\n
 with D the\nhypersurface defined by f=0.\n\nThe relation is expressed by s
 ome spectral sequences\, which may be\nused on one hand to determine the\n
 filtration P in many cases for curves and surfaces\, and on the other\nhan
 d to obtain information about\nthe syzygies involving the partial derivati
 ves of the polynomial f.\n\nThe case of a nodal hypersurface D is treated 
 in terms of the\ndefects of linear systems of hypersurfaces\nof various de
 grees passing through the nodes of D. When D is a\nnodal surface in P^3\,\
 nwe show that F^2H3(U) is not equal to P^2H3(U)\nas soon as the degree of 
 D is\nat least 4.
LOCATION:MR13\, CMS
END:VEVENT
END:VCALENDAR