The Hilbert scheme of degree two curves and certain ropes

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We study families of ropes of any codimension that are supported on lines. In particular, this includes all non-reduced curves of degree two. 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.

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Algebraic Geometry, Commutative Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/69401

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311537
 http://arxiv.org/abs/math/0311537

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arXiv