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SUMMARY:Complete intersections of quadrics - Nicolas Addington (Imperial)
DTSTART:20101103T141500Z
DTEND:20101103T151500Z
UID:TALK27347@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:There is a long-studied correspondence between intersections o
 f two\nquadrics and hyperelliptic curves.  It was first noticed by Weil in
  the\n50s and has since been a testbed for many theories: Hodge theory and
 \nmotives in the 70s\, derived categories in the 90s\,\nFloer theory and\n
 mirror symmetry today.  The two spaces are connected by some moduli\nprobl
 ems with a very classical flavor\, involving lots of lines on\nquadrics\, 
 or more fashionably by matrix factorizations.\n\nThe story extends easily 
 to intersections of three quadrics and double\ncovers of P^2\, but going t
 o four quadrics\, the double cover becomes\nsingular.  I produce a non-Kah
 ler resolution of singularities with a\nclear geometric meaning\, and rela
 te its derived category to that of the\nintersection.  As a special case I
  get a pair of derived-equivalent\nCalabi-Yau 3-folds\, which are of inter
 est in mirror symmetry.\n
LOCATION:MR13\, CMS
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