Geodesic
Lower deformations of isolated hypersurface singularities
Algebra i analiz, Tome 11 (1999) no. 5, pp. 221-249.

Voir la notice de l'article provenant de la source Math-Net.Ru

For a smooth real or complex algebraic variety $V$ and a hypersurface $W\subset V$ with isolated singular points, the deformations of these singular points are studied that can be realized by variation of $W$ in the linear system $|W|$. For isolated singularities of hypersurfaces, lower deformations are introduced, which have an explicit topologicalanalytic description. Under some conditions, it is shown that such deformations can be realized independently even if the linear system $|W|$ is not a joint versal deformation of all singular points of $W$. Several applications of lower deformations are given, including the construction of divisors with prescribed isolated singularities and the construction of real algebraic curves with prescribed topology.
Keywords: Isolated singularities, complex algebraic varieties, real algebraic curves. 
@article{AA_1999_11_5_a10,
     author = {E. Shustin},
     title = {Lower deformations of isolated hypersurface singularities},
     journal = {Algebra i analiz},
     pages = {221--249},
     publisher = {mathdoc},
     volume = {11},
     number = {5},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_1999_11_5_a10/}
}
TY  - JOUR
AU  - E. Shustin
TI  - Lower deformations of isolated hypersurface singularities
JO  - Algebra i analiz
PY  - 1999
SP  - 221
EP  - 249
VL  - 11
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_1999_11_5_a10/
LA  - en
ID  - AA_1999_11_5_a10
ER  - 
%0 Journal Article
%A E. Shustin
%T Lower deformations of isolated hypersurface singularities
%J Algebra i analiz
%D 1999
%P 221-249
%V 11
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_1999_11_5_a10/
%G en
%F AA_1999_11_5_a10
E. Shustin. Lower deformations of isolated hypersurface singularities. Algebra i analiz, Tome 11 (1999) no. 5, pp. 221-249. http://geodesic.mathdoc.fr/item/AA_1999_11_5_a10/