Geometry on nodal curves II: cycle map and intersection calculus

2004/10/05 by Ziv Ran, Ran, Ziv
Mathematics · #14C05 #14N10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C05 #msc:14N10

paper · pdf · doi:10.48550/arxiv.math/0410120

32 pages amstex

arxiv created 2004/10/05 · arxiv updated 2009/12/01

Abstract

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.

Related

• Geometry and intersection theory on Hilbert schemes of families of nodal curves
• Cycle map on Hilbert schemes of nodal curves
• Structure of the cycle map for Hilbert schemes of families of nodal curves
• A note on Hilbert schemes of nodal curves
• Geometry on nodal curves