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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

Dates:

Date	Event
2006	Published

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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