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Antonio Campillo Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Foliations in the Plane Uniquely Determined by Minimal Subschemes of its Singularities

Author : Jorge Olivares

Published in: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Publisher: Springer International Publishing

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Abstract

Let \( \mathbb {P}^n \) be the projective space over an algebraically closed ground field K. In a previous paper, we have shown that the space of foliations by curves of degree greater than or equal to two which are uniquely determined by a subscheme of minimal degree of its scheme of singularities, contains a nonempty Zariski-open subset and hence, that the set of non-degenerate foliations with this property contains a Zariski-open subset. Moreover, we posed the question whether every non-degenerate foliation in \( \mathbb {P}^2 \) has this property. In this paper, we prove that this is true, in \( \mathbb {P}^2 \), in degrees 4 and 5.

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previous chapter On the Milnor Formula in Arbitrary Characteristic
next chapter Newton Transformations and the Motivic Milnor Fiber of a Plane Curve
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Metadata
Title
Foliations in the Plane Uniquely Determined by Minimal Subschemes of its Singularities
Author
Jorge Olivares
Copyright Year
2018
Book
Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Print ISBN: 978-3-319-96826-1

Electronic ISBN: 978-3-319-96827-8

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-96827-8_6

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