Documents  58K40 | enregistrements trouvés : 5

Algebraic and Complex Geometry

Let $(X,0)$ be an ICIS of dimension $2$ and let $f :(X,0)\to\mathbb{C} ^2$ be a map germ with an isolated instability. Given $F : (\mathcal{X} , 0) \to (\mathbb{C} \times \mathbb{C}^2, 0)$ a stable unfolding of $f$, we look to the invariants related to the family $f_s$ and we find relations between them. We obtain necessary and sufficient conditions for $F$ to be Whitney equisingular. (Joint work with B. Orfice-Okamoto and J. N. Tomazella)

32S30 ; 58K15 ; 58K40 ; 32S05

... Lire [+]

Algebraic and Complex Geometry

Given a space curve, the surface ruled by tangent lines to the curve is called the tangent surface or the tangent developable to the curve. Tangent surfaces were studied by many mathemati- cians, Euler, Monge, Cayley, etc. The tangent surface has necessarily singularities along the original curve (curve of regression). The singularities are classified by Cleave, Mond, Arnold, Shcherbak and so on. In this talk we provide several generalisations of the known classification results. In particular we consider, in one direction, tangent surfaces to possibly singular curves in an ambient space of any dimension with any affine connection. In another direction, we study "abnormal" tangent surfaces to integral curves of a Cartan distribution in five space. The exposition will be performed via a generalised notion of "frontal". Given a space curve, the surface ruled by tangent lines to the curve is called the tangent surface or the tangent developable to the curve. Tangent surfaces were studied by many mathemati- cians, Euler, Monge, Cayley, etc. The tangent surface has necessarily singularities along the original curve (curve of regression). The singularities are classified by Cleave, Mond, Arnold, Shcherbak and so on. In this talk we provide several generalisations ...

53A20 ; 57R45 ; 58K40

... Lire [+]

- xvii; 312 p.
ISBN 978-0-8218-3319-3

Graduate studies in mathematics , 0083

Localisation : Collection 1er étage;Réserve

fonction de plusieurs variables complexes # singularités # invariant d'anneaux locaux analytiques # fibration de Milnor # surface de Riemann # fonction holomorphe # classification de singularités # déformation de singularités

32-01 ; 32S10 ; 32S55 ; 58K40 ; 58K60

... Lire [+]

- xv; 566 p.
ISBN 978-3-030-34439-9

Grundlehren der mathematischen wissenschaften , 0357

Localisation : Collection 1er étage

singularité des applications # théorie de Thom-Mather # équivalence droite-gauche # équivalence de contact # stabilité # dépliage vertical # champs et flux vectoriels # structure conique locale # singularité de Thom-Boardman # stabilité topologique # groupe algébrique unipotent # espace critique # discriminant # ensemble de bifurcations # espace tangent logarithmique # transversalité logarithmique # perturbation stable # nombre de Milnor image # nombre de Milnor discriminant # diviseur libre et presque libre # intersection complète # idéal d'ajustement # idéal de conducteur # espace à points multiples # théorie des noeuds # mouvement de Reidemeister # condition de rang # hypersurface paramétrée # module maximal de Cohen-Macaulay # dualité # anneau de Gorenstein # module canonique # point triple singularité des applications # théorie de Thom-Mather # équivalence droite-gauche # équivalence de contact # stabilité # dépliage vertical # champs et flux vectoriels # structure conique locale # singularité de Thom-Boardman # stabilité topologique # groupe algébrique unipotent # espace critique # discriminant # ensemble de bifurcations # espace tangent logarithmique # transversalité logarithmique # perturbation stable # nombre de Milnor image # ...

14A10 ; 14B05 ; 14B07 ; 14J17 ; 14B10 ; 13H10 ; 58K15 ; 58K40 ; 58K05 ; 58K60 ; 58K70 ; 58K25 ; 32S05 ; 32S25 ; 32S55 ; 32S60 ; 57K10

... Lire [+]