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DEFORMATIONS OF FUNCTIONS AND $F$-MANIFOLDS

Published online by Cambridge University Press:  19 December 2006

IGNACIO DE GREGORIO
IGNACIO DE GREGORIO
Affiliation:
University of Warwick, Mathematics Institute, Coventry CV4 7AL, United Kingdomignacio@maths.warwick.ac.uk
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Abstract

We study deformations of functions on isolated singularities. A unified proof of the equality of Milnor and Tjurina numbers for functions on isolated complete intersections singularities and space curves is given. As a consequence, the base space of their miniversal deformations is endowed with the structure of an $F$-manifold, and we can prove a conjecture of V. Goryunov, stating that the critical values of the miniversal unfolding of a function on a space curve are generically local coordinates on the base space of the deformation.

Keywords

32S05
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 966 - 978
Copyright
The London Mathematical Society 2006

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Footnotes

Partially suppported by EPSRC grant (00801853), EU mobility project OMATS (HPMT-CT-2000-00104) and University of Warwick Research Fellowship Scheme.