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THE HILBERT SCHEME OF DEGREE TWO CURVES AND CERTAIN ROPES

2006; World Scientific; Volume: 17; Issue: 07 Linguagem: Inglês

10.1142/s0129167x06003692

1793-6519

Uwe Nagel, Roberto Notari, Maria Luisa Spreafico,

Homotopy and Cohomology in Algebraic Topology

We study families of ropes of any codimension that are supported on lines. We construct suitable smooth parameter spaces and conclude that all ropes of fixed degree and genus lie in the same component of the corresponding Hilbert scheme. We show that this component is generically smooth if the genus is small enough unless the characteristic of the ground field is two and the curves under consideration have degree two. In this case the component is non-reduced.