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SUMMARY:Curve counting on surfaces - Martijn Kool (Imperial College)
DTSTART:20121121T141500Z
DTEND:20121121T151500Z
UID:TALK41177@talks.cam.ac.uk
CONTACT:Caucher Birkar
DESCRIPTION:Counting nodal curves in (sufficiently ample) linear systems |
 L| on smooth projective surfaces S is a problem with a long history. The G
 öttsche conjecture\, now proved by several people\, states that these cou
 nts are universal and only depend on c_1(L)^2\, c_1(L)⋅c_1(S)\,\nc_1(S)^
 2 and c_2(S). We link this classical curve count to certain Gromov-Witten 
 and stable pair invariants (with many point insertions) on S. This can be 
 see as version of the MNOP conjecture for the canonical bundle K_S. Droppi
 ng the ``sufficiently ample'' condition on\nL\, we show stable pair invari
 ants of S can still be computed and are also universal and topological. Th
 is is joint work with R. P. Thomas.
LOCATION:MR 13\, CMS
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