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Deformations of Functions and F ‐Manifolds
Author(s) -
de Gregorio Ignacio
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306018935
Subject(s) - mathematics , gravitational singularity , conjecture , base (topology) , manifold (fluid mechanics) , space (punctuation) , pure mathematics , mathematics subject classification , function (biology) , mathematical analysis , mechanical engineering , linguistics , philosophy , evolutionary biology , engineering , biology
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. 2000 Mathematics Subject Classification 32S05.