A cancellation theorem for Segre classes
-- Daniel Lowengrub, February 12, 2016

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The Riemann singularity theorem is a classical theorem
relating two important objects associated to smooth curves. It
expresses the multiplicities of points on the theta divisor in terms
of the dimensions of fibers of the Abel-Jacobi map. Sebastian
Casalaina-Martin and Jesse Kass proved an analog of this for nodal
curves and conjectured what the formula should be for general planar
curves. In this talk, we will prove a theorem about Segre classes
which will allow us to generalize Fulton's proof of the Riemann
singularity theorem (and more generally, the Riemann-Kempf formula) to
arbitrary planar curves, and thus obtain the conjectured formula.