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SUMMARY:Refined curve counting on surfaces - Lothar Goettsche (ICTP\, Trie
 ste)
DTSTART:20110119T141500Z
DTEND:20110119T151500Z
UID:TALK28589@talks.cam.ac.uk
CONTACT:Burt Totaro
DESCRIPTION:The author's conjecture was recently proved:\nfor a sufficient
 ly ample line bundle L on a surface S\, the number of curves\nwith d nodes
  in a general d-dimensional linear system\ninside |L| is given by a univer
 sal polynomial\nof degree d in the four integers L.L\, L.K_S\,\nK_S.K_S\, 
 and c_2(S). In particular\, it follows\nthat these curve counts are essent
 ially\ntopological invariants\, which was not at all clear.\n\nThe talk wi
 ll suggest a possible refinement\nof these results. The idea is new enough
 \nthat it has not yet settled into a precise conjecture.
LOCATION:MR13\, CMS
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