The aim of this work is to study and describe the resolution or desingularization of irreducible quasi ordinary surfaces, following Lipman’s approach ( [6], [7]).To achieve our goal, we define the quasi ordinary surfaces and describe their parametrization by quasi ordinary branches, we also define the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, then westudy the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we define the specialtransforms of a quasi ordinary ring and show that they are again quasi ordinary.

The aim of this thesis is to describe the resolution (partial and strict) of irreducible quasi ordinary surfaces (algebroids), by Lipman's approach. To achieve our goal, we de ne to the quasi ordinary surfaces (algebroids) and describe their parametrization by quasi ordinary branches, we also de ne the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, and we study the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring (invariants that appear in these resolutions) and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we de ne the special transforms of a quasi ordinary ring and show that they are again quasi ordinary. We conclude with an example of these resolutions.

Sea S una superficie suave, proyectiva y conexa sobre C. Sea £ el sistema lineal completo de un divisor muy amplio D en S y sea d = dim(£). Para cualquier punto cerrado t e £ = Pd*, sea Ht el hiperplano en Pd correspondiente a t, Ct = Ht n S la correspondiente sección hiperplana de S, y rt el embebimiento cerrado de Ct en S. Sea As el lugar discriminante de £ parametrizando secciones hiperplanas singulares de S y U = £ \ As su complemento parametrizando secciones hiperplanas suaves de S. Sean CHo(S)deg=o y CH0(Ct)deg=0 los grupos de Chow de 0-ciclos de grado cero en S y Ct respectivamente. En esta tesis probamos que para Ct una seccion hiperplana suave de S el Gysin kernel, i.e., el kernel del Gysin homomorfismo de CH0(Ct)deg=0 a CH0(S)deg=0 inducida por rt, es una union contable de trasladados de una subvariedad abeliana At contenida en el Jacobiano Jt de la curva Ct. Luego probam...

The aim of this thesis is to describe the resolution (partial and strict) of irreducible quasi ordinary surfaces (algebroids), by Lipman's approach. To achieve our goal, we de ne to the quasi ordinary surfaces (algebroids) and describe their parametrization by quasi ordinary branches, we also de ne the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, and we study the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring (invariants that appear in these resolutions) and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we de ne the special transforms of a quasi ordinary ring and show that they are again quasi ordinary. We conclude with an example of these resolutions.

The aim of this work is to study and describe the resolution or desingularization of irreducible quasi ordinary surfaces, following Lipman’s approach ( [6], [7]).To achieve our goal, we define the quasi ordinary surfaces and describe their parametrization by quasi ordinary branches, we also define the quasi ordinary rings, local rings of the quasi ordinary irreducible surfaces, then westudy the relationship that exists between the tangent cone and singular locus of a quasi ordinary ring and the distinguished pairs of a quasi ordinary normalized branch that represents this ring. Also, we define the specialtransforms of a quasi ordinary ring and show that they are again quasi ordinary.

In this paper we prove a result on 0-cycles on surfaces as an application of the theorem on the kernel of the Gysin homomorphism of Chow groups of 0-cycles of degree zero induced by the embedding of a curve into a surface, and we study the connection of this result with Bloch’s conjecture and constant cycles curves.