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4:00 pm Friday, November 12, 2010 Special Algebraic Geometry Seminar: Universal Formulas for Counting Nodal Curves on Surfacesby
Yu-jong Tzeng (Harvard University) in HB 227- The problem of counting nodal curves on algebraic surfaces has been studied since the nineteenth century. On the projective plane, it asks how many curves defined by homogeneous degree d polynomials have only nodes as singularities and pass through points in general position. On K3 surfaces, the number of rational nodal curves was predicted by the Yau-Zaslow formula. Goettsche conjectured that for sufficiently ample line bundles L on algebraic surfaces, the numbers of nodal curves in |L| are given by universal polynomials in four topological numbers. Furthermore, based on the Yau-Zaslow formula he gave a conjectural generating function in terms of quasi -modular forms and two unknown series. In this talk, I will discuss how degeneration methods can be applied to count nodal curves and sketch my proof of Goettsche's conjecture.
Submitted by av15@rice.edu |