Refined curve counting on surfaces

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• Lothar Goettsche (ICTP, Trieste)
• Wednesday 19 January 2011, 14:15-15:15
• 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 d-dimensional 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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