The Hilbert scheme of degree two curves and certain ropes

Uwe Nagel; Roberto Notari; Maria Luisa Spreafico

doi:10.1142/S0129167X06003692

The Hilbert scheme of degree two curves and certain ropes

Uwe Nagel, Roberto Notari, Maria Luisa Spreafico

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	835-867
Number of pages	33
Journal	International Journal of Mathematics
Volume	17
Issue number	7
DOIs	https://doi.org/10.1142/S0129167X06003692
State	Published - Aug 2006

Bibliographical note

Funding Information:
The authors warmly thank INDAM-GNSAGA for partial support. The first author was also partially supported by a Faculty Summer Research Fellowship from the University of Kentucky.

Keywords

Curves
Hilbert scheme
Minimal free resolution
Normal sheaf
Ropes

ASJC Scopus subject areas

Mathematics (all)

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10.1142/S0129167X06003692

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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 = "Curves, Hilbert scheme, Minimal free resolution, Normal sheaf, Ropes",

author = "Uwe Nagel and Roberto Notari and Spreafico, {Maria Luisa}",

note = "Funding Information: The authors warmly thank INDAM-GNSAGA for partial support. The first author was also partially supported by a Faculty Summer Research Fellowship from the University of Kentucky.",

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AU - Nagel, Uwe

AU - Notari, Roberto

AU - Spreafico, Maria Luisa

N1 - Funding Information: The authors warmly thank INDAM-GNSAGA for partial support. The first author was also partially supported by a Faculty Summer Research Fellowship from the University of Kentucky.

PY - 2006/8

Y1 - 2006/8

N2 - 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.

AB - 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.

KW - Curves

KW - Hilbert scheme

KW - Minimal free resolution

KW - Normal sheaf

KW - Ropes

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ER -

The Hilbert scheme of degree two curves and certain ropes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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