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Deformations of functions and F-manifolds

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De Gregorio, Ignacio. (2006) Deformations of functions and F-manifolds. Bulletin of the London Mathematical Society, Vol.38 (No.6). pp. 966-978. ISSN 0024-6093

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Official URL: http://dx.doi.org/10.1112/S0024609306018935

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Deformations of singularities, Frobenius manifolds, Complex manifolds, Manifolds (Mathematics)
Journal or Publication Title:	Bulletin of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6093
Official Date:	2006
Volume:	Vol.38
Number:	No.6
Page Range:	pp. 966-978
Identification Number:	10.1112/S0024609306018935
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	University of Warwick, Engineering and Physical Sciences Research Council (EPSRC), Oslo Mathematics Doctoral Training Site (OMATS)
Grant number:	00801853 (EPSRC), HPMT-CT-2000-00104 (OMATS)
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URI:	http://wrap.warwick.ac.uk/id/eprint/693