Unfoldings of holomorphic foliations

The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial

Bailando con números: De los atractores al caos

El universo es un lugar desconocido y gigantesco, lleno de cosas al azar, lo que trata de entender uno, es el orden que hay detrás de ello; palabras del propio Xavier Gómez. En la charla aborda el hecho de como las matemáticas están inmersas hasta en las acciones más básicas y forman parte del instinto de muchos seres vivos. “Un águila quiere cazar a otro pájaro. Tiene que tomar en cuenta tanto su propia posición como la de su víctima, la velocidad del aire, las habilidades físicas de ambos y echar a andar toda una estrategia de cómo le va a hacer para alcanzar a su presa”, menciona. La sesión del café está acompañada por Christian Bonatti, matemático por la Universidad de Bourgogne de Dijon, Francia. Xavier Gómez Mont Avalos, es licenciado en matemáticas por la Facultad de Ciencias de la UNAM y doctor en la misma disciplina desde 1978 por la Universidad de Princeton, EUA. Ha trabajado en el Instituto de Matemáticas de la UNAM y en el Centro de Investigación en Matemáticas, en la ciudad de Guanajuato, donde es actualmente investigador. Es miembro del Sistema Nacional de Investigadores desde su fundación. Su especialidad son la Geometría y la Dinámica, ramas a las cuales ha contribuido con diversos trabajos de investigación.ITESO, A.C

Unfoldings of holomorphic foliations

The objective of this paper is to give a criterium for an unfolding of a holomorphic foliation with singularities to be holomorphically trivial

On the complex formed by contracting differential forms with a vector field on a hypersurface singularity

Let (V, 0) subset of (Cn+1, 0) bean analytic hypersurface with an isolated singularity at 0, and X = (X) over tilde \(V) a tangent vector field to V, where (X) over tilde is a holomorphic vector field in (Cn+1, 0) which has an isolated singularity at 0, The homological index of X at 0 can be defined ([4]) as the Euler characteristic of the complex formed by contracting with X the Kahler differentials on V. In that complex, the homology groups are equidimensional and isomorphic to certain modules defined from the finite dimensional C-algebras associated to the jacobian ideal of the function defining V, and to the coordinates of (X) over tilde ([4]). In this paper, we present an algorithm that provides those isomorphisms in an explicit way, so making it possible to face the problem of extending the homological index to other geometric situations ([3])

On the complex formed by contracting differential forms with a vector field on a hypersurface singularity

Let (V, 0) subset of (Cn+1, 0) bean analytic hypersurface with an isolated singularity at 0, and X = (X) over tilde \(V) a tangent vector field to V, where (X) over tilde is a holomorphic vector field in (Cn+1, 0) which has an isolated singularity at 0, The homological index of X at 0 can be defined ([4]) as the Euler characteristic of the complex formed by contracting with X the Kahler differentials on V. In that complex, the homology groups are equidimensional and isomorphic to certain modules defined from the finite dimensional C-algebras associated to the jacobian ideal of the function defining V, and to the coordinates of (X) over tilde ([4]). In this paper, we present an algorithm that provides those isomorphisms in an explicit way, so making it possible to face the problem of extending the homological index to other geometric situations ([3]).Depto. de Álgebra, Geometría y TopologíaFac. de Ciencias MatemáticasTRUEpu