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This book presents fundamentals from the theory of algebraic surfaces, including areas such as rational singularities of surfaces and their relation with Grothendieck duality theory, numerical criteria for contractibility of curves on an algebraic surface, and the problem of minimal models of surfaces. In fact, the classification of surfaces is the main scope of this book and the author presents the approach developed by Mumford and Bombieri. Chapters also cover the Zariski decomposition of effective divisors and graded algebras.
The aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry. Some of these methods are illustrated in the first part through the proofs of a number of results of a rather classical flavor, involving in a crucial way the first infinitesimal neighbourhood of a given subvariety in an ambient variety. Motivated by the first part, in the second formal functions on the formal completion X/Y of X along a closed subvariety Y are studied, particularly the extension problem of formal functions to rational functions. The formal scheme X/Y, introduced to algebraic geometry by Zariski and Grothendieck in the 1950s, is an an...
Journal IV is the first publication, in a translation from the Romanian manuscript, of the journal that Mircea Eliade kept during the last seven years of his life. In this period, Eliade is ensconced as a famous scholar—his works are being translated into many languages and books about him arrive regularly in the mail. His encounters with scholars of like repute are recorded in the journal; after a party in Paris, Eliade shares a taxi with Claude Lévi-Strauss and inadvertently makes off with his raincoat. Running like a fault line through the peak of his success, however, is Eliade's painful awareness of his physical decline—failing vision, arthritic hands, and continual fatigue. Again ...
The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
This book explores an aspect of the complex cultural history of 20th-century exile: the influences of transnational experiences on the views of emigrants and exiles concerning their own academic, scientific and intellectual cultures. These essays focus on the reflections of people who left their countries during the period of 1933–1945. Many of them reconsidered their own past in the old country and compared it with their actual experiences in the adopted homeland. The individual cases presented here share a similar theoretical framework. The book is divided into two sections: the first one focuses on the German and Spanish lost project, and the second one deals with the East European proj...
Contains contributions by over 25 leading international mathematicians in the areas of commutative algebra and algebraic geometry. The text presents developments and results based on, and inspired by, the work of Mario Fiorentini. It covers topics ranging from almost numerical invariants of algebraic curves to deformation of projective schemes.
This book discusses regular powers and symbolic powers of ideals from three perspectives– algebra, combinatorics and geometry – and examines the interactions between them. It invites readers to explore the evolution of the set of associated primes of higher and higher powers of an ideal and explains the evolution of ideals associated with combinatorial objects like graphs or hypergraphs in terms of the original combinatorial objects. It also addresses similar questions concerning our understanding of the Castelnuovo-Mumford regularity of powers of combinatorially defined ideals in terms of the associated combinatorial data. From a more geometric point of view, the book considers how the relations between symbolic and regular powers can be interpreted in geometrical terms. Other topics covered include aspects of Waring type problems, symbolic powers of an ideal and their invariants (e.g., the Waldschmidt constant, the resurgence), and the persistence of associated primes.