# Structure of the cycle map for Hilbert schemes of families of nodal curves - Mathematics > Algebraic Geometry

Structure of the cycle map for Hilbert schemes of families of nodal curves - Mathematics > Algebraic Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We study the relative Hilbert scheme of a family of nodal or smooth curves,over a base of arbitrary dimension, via its birational cycle map, going tothe relative symmetric product. We show the cycle map is the blowing up of thediscriminant locus, which consists of cycles with multiple points. We determinethe relevant cotangent sheaves and complexes. We determine the structure ofcertain projective bundles called node scrolls, which play an important role inthe geometry of Hilbert schemes.

Author: ** Ziv Ran**

Source: https://arxiv.org/