4:00 pm Friday, November 12, 2010
Special Algebraic Geometry Seminar: Universal Formulas for Counting Nodal Curves on Surfaces
by
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. Host Department: Rice University-Mathematics
Submitted by av15@rice.edu |
