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arXiv:0903.3693 [math.AG]AbstractReferencesReviewsResources

Structure of the cycle map for Hilbert schemes of families of nodal curves

Ziv Ran

Published 2009-03-21, updated 2015-08-23Version 3

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 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 determine the relevant cotangent sheaves and complexes. We determine the structure of certain projective bundles called node scrolls, which play an important role in the geometry of Hilbert schemes.

Comments: To appear in Israel J. Math. arXiv admin note: text overlap with arXiv:0803.4512
Categories: math.AG
Subjects: 14N99, 14H99
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