Curve counting on surfaces
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 Martijn Kool (Imperial College)
 Wednesday 21 November 2012, 14:1515:15
 MR 13, CMS.
If you have a question about this talk, please contact Caucher Birkar.
Counting nodal curves in (sufficiently ample) linear systems L on smooth projective surfaces S is a problem with a long history. The Göttsche conjecture, now proved by several people, states that these counts are universal and only depend on c_1(L)^{2, c_1(L)⋅c_1(S),
c_1(S)}2 and c_2(S). We link this classical curve count to certain GromovWitten 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. Dropping the ``sufficiently ample’’ condition on
L, we show stable pair invariants of S can still be computed and are also universal and topological. This is joint work with R. P. Thomas.
This talk is part of the Algebraic Geometry Seminar series.
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