Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Mather-Yau theorem in positive characteristic


Authors: Gert-Martin Greuel and Thuy Huong Pham
Journal: J. Algebraic Geom. 26 (2017), 347-355
DOI: https://doi.org/10.1090/jag/669
Published electronically: September 23, 2016
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Abstract | References | Additional Information

Abstract: The well-known Mather-Yau theorem says that the isomorphism type of the local ring of an isolated complex hypersurface singularity is determined by its Tjurina algebra. It is also well known that this result is wrong as stated for power series $ f$ in $ K[[{\bf x}]]$ over fields $ K$ of positive characteristic. In this note we show that, however, also in positive characteristic the isomorphism type of an isolated hypersurface singularity $ f$ is determined by an Artinian algebra, namely by a ``higher Tjurina algebra'' for sufficiently high index, for which we give an effective bound. We prove also a similar version for the ``higher Milnor algebra" considered as a $ K[[f]]$-algebra.


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Additional Information

Gert-Martin Greuel
Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger Str., 67663 Kaiserslautern, Germany
Email: greuel@mathematik.uni-kl.de

Thuy Huong Pham
Affiliation: Fachbereich Mathematik, Universität Kaiserslautern, Erwin-Schrödinger Str., 67663 Kaiserslautern, Germany
Address at time of publication: Department of Mathematics, Quy Nhon University, 170 An Duong Vuong Street, Quy Nhon City, Vietnam
Email: phamthuyhuong@qnu.edu.vn

DOI: https://doi.org/10.1090/jag/669
Received by editor(s): April 16, 2014
Received by editor(s) in revised form: July 31, 2014, and August 6, 2014
Published electronically: September 23, 2016
Additional Notes: The second author was supported by DAAD (Germany).
Article copyright: © Copyright 2016 University Press, Inc.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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Online ISSN 1534-7486; Print ISSN 1056-3911
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