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On vanishing inflection points of plane curves

Mauricio Garay (2002)

Annales de l’institut Fourier

We study the local behaviour of inflection points of families of plane curves in the projective plane. We develop normal forms and versal deformation concepts for holomorphic function germs f : ( 2 , 0 ) ( , 0 ) which take into account the inflection points of the fibres of f . We give a classification of such function- germs which is a projective analog of Arnold’s A,D,E classification. We compute the versal deformation with respect to inflections of Morse function-germs.

Smoothing of rational m-ropes

Edoardo Ballico, Elizabeth Gasparim, Thomas Köppe (2009)

Open Mathematics

In a recent paper, Gallego, González and Purnaprajna showed that rational 3-ropes can be smoothed. We generalise their proof, and obtain smoothability of rational m-ropes for m ≥ 3.

The Hilbert scheme of space curves of small diameter

Jan Oddvar Kleppe (2006)

Annales de l’institut Fourier

This paper studies space curves C of degree d and arithmetic genus g , with homogeneous ideal I and Rao module M = H * 1 ( I ˜ ) , whose main results deal with curves which satisfy 0 Ext R 2 ( M , M ) = 0 (e.g. of diameter, diam M 2 ). For such curves we find necessary and sufficient conditions for unobstructedness, and we compute the dimension of the Hilbert scheme, H ( d , g ) , at ( C ) under the sufficient conditions. In the diameter one case, the necessary and sufficient conditions coincide, and the unobstructedness of C turns out to be equivalent to the...

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