Structure of the Cycle Map for Hilbert Schemes of Families of Nodal Curves
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چکیده
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 study certain loci called node scrolls which play in important role in the geometry of the cycle map.
منابع مشابه
Geometry and Intersection Theory on Hilbert Schemes of Families of Nodal Curves
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 work out the action of the blowup or ’discriminant’ polarization on some natural cycles in th...
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