7 citations · 13 across the 5 of their papers we have counts for
15 papers · 1 filter
Geometry on nodal curves II: cycle map and intersection calculus
Ziv Ran
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 b…
A note on Hilbert schemes of nodal curves
Ziv Ran
We study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then ex…
Cycle map on Hilbert schemes of nodal curves
Ziv Ran
We study the structure of the relative Hilbert scheme for a family of nodal (or smooth) curves via its natural cycle map to the relative symmetric product. We show that the cycle m…
Normal bundles of rational curves in projective spaces
Ziv Ran
We determine the splitting (isomorphism) type of the normal bundle of a generic genus-0 curve with 1 or 2 components in any projective space, as well as the (sometimes nontrivial)…
Geometry on nodal curves
Ziv Ran
Given a family of nodal curves, we construct canonically and compatibly with base-change, via an explicit blow-up of the Cartesian product , a family parame…
Enumerative geometry of divisorial families of rational curves
Ziv Ran
This revision contains some additional corrections and references, including a reference to Zeuthen suggested by Kleiman. For possible subsequent revisions, check http://math.ucr.e…