Refined curve counting on surfaces
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 Lothar Goettsche (ICTP, Trieste)
 Wednesday 19 January 2011, 14:1515:15
 MR13, CMS.
If you have a question about this talk, please contact Burt Totaro.
The author’s conjecture was recently proved:
for a sufficiently ample line bundle L on a surface S, the number of curves
with d nodes in a general ddimensional linear system
inside L is given by a universal polynomial
of degree d in the four integers L.L, L.K_S,
K_S.K_S, and c_2(S). In particular, it follows
that these curve counts are essentially
topological invariants, which was not at all clear.
The talk will suggest a possible refinement
of these results. The idea is new enough
that it has not yet settled into a precise conjecture.
This talk is part of the Algebraic Geometry Seminar series.
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