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DEFORMATIONS OF DIFFERENTIAL ARCS

Part of: Local theory Differential and difference algebra Birational geometry

Published online by Cambridge University Press:  16 August 2016

DAVID BOURQUI  and
JULIEN SEBAG
DAVID BOURQUI*
Affiliation:
Institut de recherche mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France email david.bourqui@univ-rennes1.fr
JULIEN SEBAG
Affiliation:
Institut de recherche mathématique de Rennes, UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France email julien.sebag@univ-rennes1.fr
*
✉david.bourqui@univ-rennes1.fr
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Abstract

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Let $k$ be field of characteristic zero. Let $f\in k[X,Y]$ be a nonconstant polynomial. We prove that the space of differential (formal) deformations of any formal general solution of the associated ordinary differential equation $f(y^{\prime },y)=0$ is isomorphic to the formal disc $\text{Spf}(k[[Z]])$.

Keywords

arc schemedifferential algebraformal neighbourhoodautonomous ordinary differential equation

MSC classification

Primary: 14E18: Arcs and motivic integration
Secondary: 14B20: Formal neighborhoods 12H05: Differential algebra
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 94 , Issue 3 , December 2016 , pp. 405 - 410
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

References

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