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CATEGORIES:Algebraic Geometry Seminar
SUMMARY:Koszul complexes and pole order filtrations for pr
ojective hypersurfaces - Alex Dimca (Nice)
DTSTART;TZID=Europe/London:20111109T141500
DTEND;TZID=Europe/London:20111109T151500
UID:TALK33069AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/33069
DESCRIPTION:I'll discuss the interplay between the cohomology
of the\nKoszul complex\nof the partial derivatives
of a homogeneous polynomial f and the\npole order
filtration P\non the cohomology of the open set U
=P^n-D\,\nwith D the\nhypersurface defined by f=0.
\n\nThe relation is expressed by some spectral seq
uences\, which may be\nused on one hand to determi
ne the\nfiltration P in many cases for curves and
surfaces\, and on the other\nhand to obtain inform
ation about\nthe syzygies involving the partial de
rivatives of the polynomial f.\n\nThe case of a no
dal hypersurface D is treated in terms of the\ndef
ects of linear systems of hypersurfaces\nof variou
s degrees passing through the nodes of D. When D i
s a\nnodal surface in P^3\,\nwe show that F^2H3(U)
is not equal to P^2H3(U)\nas soon as the degree o
f D is\nat least 4.
LOCATION:MR13\, CMS
CONTACT:Burt Totaro
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