The focus of this volume lies on singularity theory in algebraic geometry. It includes papers documenting recent and original developments and methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The papers originate from the Third International Conference on Algebraic Geometry held in La Rábida, Spain, in December 1991. Since then, the articles have undergone a meticulous process of refereeing and improvement, and they have been organized into a comprehensive account of the state of the art in this field.

Klappentext

The volume contains both general and research papers. Among the first ones are papers showing recent and original developments or methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The research papers deal on topics related to, or close to, those listed_above. The contributions are organized in three parts according to their contents. Part I presents a set of papers on resolution of singularities, a topic of renewed activity. It deals with important topics of current interest, such as canonical, algorithmic, combinatorial and graphical procedures (Villamayor, Oka, Marijmin), as well as special results on desingularization in characteristic p (Cossart, Moh), and connections between resolution and structure of the space of arcs through a singularity (Gonz81ez-Sprinberg-Lejeune-Jalabert). Part II contains a series of papers on the study~of singularities and its connections with differential systems and deformation or perturbation theo­ ries. Two expository papers (Maisonobe-Briam;on, :'vlebkhout) describe, in an algebro-geometric way, the interaction between singularities and D-module t.he­ ory including recent progress on Bernstein polynomials and Newton polygon techniques. Geometry of foliations (Henaut, Garcfa-Reguera), polar varieties and stratifications (Hajto) are also topics treated here. Two other papers (Wall, Greuel-Pfister) deal with quasihomogeneous singularities in the contexts of per­ turbations and moduli spaces. Globalization of deformations of singularities (de Jong) and determination of complex topology from the real one (~10nd) com­ plete this series of papers. Part III consists of papers on algebraic geometry of curves and surfaces.

Inhalt
I Resolution of Singularities.- Désingularisation en dimension 3 et caractéristique p.- Sur l'espace des courbes tracées sur une singularité.- Blowing up acyclic graphs and geometrical configurations.- On a Newton polygon approach to the uniformization of singularities of characteristic p.- Geometry of plane curves via toroidal resolution.- to the algorithm of resolution.- II Complex Singularities and Differential Systems.- Polarity with respect to a foliation.- On moduli spaces of semiquasihomogeneous singularities.- Stratification Properties of Constructible Sets.- On the linearization problem and some questions for webs in ?2.- Globalization of Admissible Deformations.- Caractérisation géométrique de l'existence du polynôme de Bernstein relatif.- Le Polygone de Newton d'un DX-module.- How good are real pictures?.- Weighted homogeneous complete intersections.- III Curves and Surfaces.- Degree 8 and genus 5 curves in ?3 and the Horrocks-Mumford bundle.- Irreducible Polynomials of k((X))[Y].- Examples of Abelian Surfaces with Polarization type (1,3).- Semigroups and Clusters at Infinity.- Cubic surfaces with double points in positive characteristic.- On the classification of reducible curve singularities.