7 papers
Lagrangian submanifolds and Lefschetz pencils
Denis Auroux, Vicente Muñoz, Francisco Presas
Given a Lagrangian submanifold in a symplectic manifold and a Morse function on the submanifold, we show that there is an isotopic Morse function and a symplectic Lefschetz pencil…
Codimension one symplectic foliations
Omegar Calvo, Vicente Munoz, Francisco Presas
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
Semipositive bundles and Brill-Noether theory
Vicente Munoz, Francisco Presas
We prove a Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles and over a complex manifold under the condition that…
Submanifolds of symplectic manifolds with contact border
Francisco Presas
We construct symplectic submanifolds of symplectic manifolds with contact border. The boundary of such submanifolds is shown to be a contact submanifold of the contact border. We a…
Lefschetz type pencils on contact manifolds
Francisco Presas
We define the concept of Lefschetz contact pencil and we show the existence of such structures on any contact manifold. The main idea of the proof is a generalization of the Donald…
Almost holomorphic embeddings in Grassmannians with applications to singular simplectic submanifolds
Vicente Muñoz, Fran Presas, Ignacio Sols
We use Donaldson's approximately holomorphic techniques to build embeddings of a closed symplectic manifold with symplectic form of integer class in the grassmannians Gr(r,N). We a…