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Curve counting on surfaces
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 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. 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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