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Counting curves with tangency conditions

Charles Cadman, University of Michigan

Abstract:
Gromov-Witten theory has been used to tackle problems in enumerative geometry
ever since Kontsevich found a nice recursion computing the number of rational
degree d plane curves passing through 3d-1 general points. The Gromov-Witten
theory of stacks is a recent development, and I used it to count rational plane
curves which are tangent to a smooth cubic at a specified number of points.
More precisely, there are explicit recursions which generalize Kontsevich's
recursion and reduce everything to how many lines pass through two general
points. It is possible to combine this with a technique used by Caporaso
and Harris to generalize and simplify the result. I will state the result and
give an outline of the proof.