Contributions To Complex Analysis And Analytic Geometry

​This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations. ​

The articles in this volume cover some developments in complex analysis and algebraic geometry. The book is divided into three parts. Part I includes topics in the theory of algebraic surfaces and analytic surface. Part II covers topics in moduli and classification problems, as well as structure theory of certain complex manifolds. Part III is devoted to various topics in algebraic geometry analysis and arithmetic. A survey article by Ueno serves as an introduction to the general background of the subject matter of the volume. The volume was written for Kunihiko Kodaira on the occasion of his sixtieth birthday, by his friends and students. Professor Kodaira was one of the world's leading mathematicians in algebraic geometry and complex manifold theory: and the contributions reflect those concerns.

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Preface of the Editors Ce volume prend sa source dans le Colloque en l'honneur de Pierre Dolbeault, organise a l'occasion de son depart a la retraite, a !'initiative des Universites de Paris 6 et de Poitiers. Ce colloque, consacre a l' Analyse Complexe et a la Geometrie Analytique, s'est tenu a Paris, sur le campus de l'Universite Pierreet Marie Curie, du 23 au 26 Juin 1992.11 areuni autour de ces themes une centaine de congressistes, dont de nombreux mathematiciens etrangers (Allemagne, Argentine, Canada, Etats-Unis, Islande, Italie, Pologne, Roumanie, Russie, Suede). Nous avons souhaite prolanger cet hommage par la publication d'un volume dedie a Pierre Dolbeault. Le present recueil d'articles ne constitue pas strictement les actes du Colloque. Nous avons voulu qu'il rassemble uniquement des articles originaux ou synthetiques, qui illustrent l' ceuvre scientifique de Pierre Dolbeault a travers les themes abordes ou la personnalite de leurs auteurs. Nous remercions les conferenciers qui ont bien voulu contribuer a cet ouvrage, et Klas Diederich de l'avoir accueilli dans la collection "Aspects of Mathematics" qu'il dirige. Au nom du Comite d'Organisation du Colloque (C. Laurent-Thiebaut, J. Le Potier, J.B. Poly, J.P. Vigue et nous-memes), nous remercions les institutions qui nous ont apporte leur aide financiere et materielle: les Universites Paris 6 et de Poitiers, la Direction de la Recherche et des Etudes Doctorales, le Centre National de la Recherche Scientifique et le Ministere de la Recherche et de la Technologie.

This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are based upon their presentations at the 10th Korean Conference on Several Complex Variables (KSCV10), held as a satellite conference to the International Congress of Mathematicians (ICM) 2014 in Seoul, Korea. SCV has been the term for multidimensional complex analysis, one of the central research areas in mathematics. Studies over time have revealed a variety of rich, intriguing, new knowledge in complex analysis and geometry of analytic spaces and holomorphic functions which were "hidden" in the case of complex dimension one. These new theories have significant intersections with algebraic geometry, differential geometry, partial differential equations, dynamics, functional analysis and operator theory, and sheaves and cohomology, as well as the traditional analysis of holomorphic functions in all dimensions. This book is suitable for a broad audience of mathematicians at and above the beginning graduate-student level. Many chapters pose open-ended problems for further research, and one in particular is devoted to problems for future investigations.