Geometry on nodal curves II: cycle map and intersection calculus

Details Geometry on nodal curves II: cycle map and intersection calculus Geometry on nodal curves II: cycle map and intersection calculus

2004-10-05

arxiv.org/abs/math/0410120v1

Mathematics

Algebraic Geometry

32 pages amstex

Scientific paper

We study the relative Hilbert scheme of a family of nodal (or smooth) curves via its (birational) cycle map, going to the relative symmetric product. We show the cycle map is the blowing up of the discriminant locus, which consists of cycles with multiple points. We derive an intersection calculus for Chern classes of tautological bundles on the relative Hilbert scheme, which has applications to enumerative geometry.

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