Geometry of obstructed families of curves

Anna Gourevitch

doi:10.1016/j.jpaa.2006.11.013

Geometry of obstructed families of curves

Anna Gourevitch^*

^*Corresponding author for this work

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

2 Scopus citations

Abstract

We study certain equisingular families of curves with quasihomogeneous singularity of minimal obstructness (i.e. h¹ = 1). We show that our families always have expected codimension. Moreover they are either non-reduced with smooth reduction or decompose into two smooth components of expected codimension that intersect non-transversally or are reduced irreducible non-smooth varieties which have smooth singular locus with sectional singularity of type A₁. On the other hand there is an example of an equisingular family of curves with multiple quasihomogeneous singularities of minimal obstructness which is smooth but has wrong codimension. We use algorithms of computer algebra as a technical tool.

Original language	English
Pages (from-to)	721-734
Number of pages	14
Journal	Journal of Pure and Applied Algebra
Volume	210
Issue number	3
DOIs	https://doi.org/10.1016/j.jpaa.2006.11.013
State	Published - Sep 2007
Externally published	Yes

Bibliographical note

Funding Information:
The author was supported by the Hermann-Minkowski-Minerva Center for Geometry at the Tel-Aviv University, by the grant no. 465/04 from the Israel Science Foundation. I thank Prof. Evgenii Shustin for supervising this work. I would also like to thank my friend Dmitry Gourevitch for helpful discussions. I thank the referee for useful remarks.

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10.1016/j.jpaa.2006.11.013

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title = "Geometry of obstructed families of curves",

abstract = "We study certain equisingular families of curves with quasihomogeneous singularity of minimal obstructness (i.e. h1 = 1). We show that our families always have expected codimension. Moreover they are either non-reduced with smooth reduction or decompose into two smooth components of expected codimension that intersect non-transversally or are reduced irreducible non-smooth varieties which have smooth singular locus with sectional singularity of type A1. On the other hand there is an example of an equisingular family of curves with multiple quasihomogeneous singularities of minimal obstructness which is smooth but has wrong codimension. We use algorithms of computer algebra as a technical tool.",

author = "Anna Gourevitch",

note = "Funding Information: The author was supported by the Hermann-Minkowski-Minerva Center for Geometry at the Tel-Aviv University, by the grant no. 465/04 from the Israel Science Foundation. I thank Prof. Evgenii Shustin for supervising this work. I would also like to thank my friend Dmitry Gourevitch for helpful discussions. I thank the referee for useful remarks.",

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Geometry of obstructed families of curves

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