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THE HILBERT SCHEME OF DEGREE TWO CURVES AND CERTAIN ROPES

UWE NAGEL

Department of Mathematics, University of Kentucky, 715 Patterson Office Tower, Lexington, KY 40506-0027, USA

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ROBERTO NOTARI

Dipartimento di Matematica, Politecnico di Torino, I-10129 Torino, Italy

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MARIA LUISA SPREAFICO

Dipartimento di Matematica, Politecnico di Torino, I-10129 Torino, Italy

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https://doi.org/10.1142/S0129167X06003692Cited by:3 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: Primary 14C05, Primary 14H10, Primary 14H45, Secondary 13D02

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