https://uvadoc.uva.es/handle/10324/1194 Dpto. Álgebra, Análisis Matemático, Geometría y Topología - Capítulos de monografías 2026-04-07T19:50:35Z https://uvadoc.uva.es/handle/10324/71759 The question of R. Thom of existence of invariant hypersurface for germs of holomorphic codimension one foliations is a leitmotiv in the theory. In these notes, we give a panorama of the state of art of this question, where the reduction of singularities plays a central role. We start with an elementary and detailed study of the final points expected after reduction of singularities, focusing the attention on concepts and properties concerning invariant hypersurfaces. 2024-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/31741 The bilinear form with associated identity matrix is used in coding theory to define the dual code of a linear code, also it endows linear codes with a metric space structure. This metric structure was studied for generalized toric codes and a characteristic decomposition was obtained, which led to several applications as the construction of stabilizer quantum codes and LCD codes. In this work, we use the study of bilinear forms over a finite field to give a decomposition of an arbitrary linear code similar to the one obtained for generalized toric codes. Such a decomposition, called the geometric decomposition of a linear code, can be obtained in a constructive way; it allows us to express easily the dual code of a linear code and provides a method to construct stabilizer quantum codes, LCD codes and in some cases, a method to estimate their minimum distance. The proofs for characteristic 2 are different, but they are developed in parallel. 2018-01-01T00:00:00Z https://uvadoc.uva.es/handle/10324/31740 Linear ramp secret sharing schemes are given by a pair of nested codes. In this work algebraic geometry codes are considered. We found sufficient conditions for qualified or forbidden sets by using geometric properties of the set of points. This article considers both classical schemes and quantum schemes. 2017-01-01T00:00:00Z