SGAyAp - Charlas Futuras
Botbol, Nicolás (nbotbol@dm.uba.ar): Implicitacion de hipersuperficies en espacios proyectivos. Parte II
En esta charla daremos un breve paneo a algunas tecnicas de implicitacion de hipersuperfies mediante herramientas de algebras conmutativa y homologica. Mencionaremos los metodos recientemente desarrollados en el area de implicitacion para el caso de una aplicacion racional f:P^n ---> P^(n+1), y posteriormente estudiaremos como se comportan estas tecnicas para el caso f:P^n ---> (P^1)^(n+1). Finalmente, veremos algunas aplicaciones al calculo de discriminantes, al estilo de Horn y Kapranov.
Galigo, André (Andre.GALLIGO@unice.fr): Resultants and the computation of intersection and selfintersection loci of parameterized surfaces.
I will recall and present several approaches relying on algebraic elimination (and more precisely resultant) techniques, marching, subdivisions, use of the Bernstein bases, to compute either the intersection locus of two parameterized surfaces or the selfintersection locus of a parameterized surface.
Then I will present in more detail a recent joint work with L. Buse and M. Elkadi on resultants of systems of polynomials with separated variables.
Such systems are simple sparse bivariate ones but resemble to univariate systems:
Interesting structures for generalized Sylvester and Bezoutian matrices can be explicited.
One can take advantage of these structures to represent the objects and speed up the computations.
Dohm, Marc (marcdohm@gmail.com): Implicitization of canal surfaces
I will present some joint work with Severinas Zube (Vilnius
University).
A canal surface is defined as the envelope of a family of spheres
moving along a space curve.
I will talk about a geometric approach (based on Lie and Laguerre
Sphere Geometry) that relates this surface to a certain curve in P^5. This allows us to represent the implicit equation of such a surface as the resultant of a so-called mu-basis, which can be computed efficiently with linear algebra methods (such as the Smith normal form). If time permits, I will also talk about a formula for the degree of the canal surface and explain how the mu-basis can be used to give a parametrization of the surface of minimal degree.
Botbol, Nicolás (nbotbol@dm.uba.ar): Implicitacion de hipersuperficies en espacios proyectivos. Parte II
En esta charla daremos un breve paneo a algunas tecnicas de implicitacion de hipersuperfies mediante herramientas de algebras conmutativa y homologica. Mencionaremos los metodos recientemente desarrollados en el area de implicitacion para el caso de una aplicacion racional f:P^n ---> P^(n+1), y posteriormente estudiaremos como se comportan estas tecnicas para el caso f:P^n ---> (P^1)^(n+1). Finalmente, veremos algunas aplicaciones al calculo de discriminantes, al estilo de Horn y Kapranov.
Galigo, André (Andre.GALLIGO@unice.fr): Resultants and the computation of intersection and selfintersection loci of parameterized surfaces.
I will recall and present several approaches relying on algebraic elimination (and more precisely resultant) techniques, marching, subdivisions, use of the Bernstein bases, to compute either the intersection locus of two parameterized surfaces or the selfintersection locus of a parameterized surface.
Then I will present in more detail a recent joint work with L. Buse and M. Elkadi on resultants of systems of polynomials with separated variables.
Such systems are simple sparse bivariate ones but resemble to univariate systems:
Interesting structures for generalized Sylvester and Bezoutian matrices can be explicited.
One can take advantage of these structures to represent the objects and speed up the computations.
Dohm, Marc (marcdohm@gmail.com): Implicitization of canal surfaces
I will present some joint work with Severinas Zube (Vilnius University).
A canal surface is defined as the envelope of a family of spheres moving along a space curve.
I will talk about a geometric approach (based on Lie and Laguerre Sphere Geometry) that relates this surface to a certain curve in P^5. This allows us to represent the implicit equation of such a surface as the resultant of a so-called mu-basis, which can be computed efficiently with linear algebra methods (such as the Smith normal form). If time permits, I will also talk about a formula for the degree of the canal surface and explain how the mu-basis can be used to give a parametrization of the surface of minimal degree.