The Singularities


Book Description

'This novel is essence of Banville ... a career summation' Daily Telegraph Felix Mordaunt, recently released from prison, steps from a flashy red sports car onto the estate of his youth. But there is a new family living in the drafty old house: descendants of the late, world-famous scientist Adam Godley. Felix must now vie with the idiosyncratic Godley family, with their harried housekeeper who becomes his landlady, with the recently commissioned biographer of Godley Sr., and with a wealthy and beautiful woman from his past who comes bearing an unusual request...




Introduction to Singularities


Book Description

This book is an introduction to singularities for graduate students and researchers. It is said that algebraic geometry originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. Most of them were about non-singular varieties. Singularities were considered “bad” objects that interfered with knowledge of the structure of an algebraic variety. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. Another example is that the moduli spaces of varieties have natural compactification, the boundaries of which correspond to singular varieties. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dim ensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied.




Introduction to Singularities and Deformations


Book Description

Singularity theory is a young, rapidly-growing topic with connections to algebraic geometry, complex analysis, commutative algebra, representations theory, Lie groups theory and topology, and many applications in the natural and technical sciences. This book presents the basic singularity theory of analytic spaces, including local deformation theory and the theory of plane curve singularities. It includes complete proofs.




Resolution of Singularities


Book Description

The notion of singularity is basic to mathematics. In algebraic geometry, the resolution of singularities by simple algebraic mappings is truly a fundamental problem. It has a complete solution in characteristic zero and partial solutions in arbitrary characteristic. The resolution of singularities in characteristic zero is a key result used in many subjects besides algebraic geometry, such as differential equations, dynamical systems, number theory, the theory of $\mathcal{D}$-modules, topology, and mathematical physics. This book is a rigorous, but instructional, look at resolutions. A simplified proof, based on canonical resolutions, is given for characteristic zero. There are several proofs given for resolution of curves and surfaces in characteristic zero and arbitrary characteristic. Besides explaining the tools needed for understanding resolutions, Cutkosky explains the history and ideas, providing valuable insight and intuition for the novice (or expert). There are many examples and exercises throughout the text. The book is suitable for a second course on an exciting topic in algebraic geometry. A core course on resolutions is contained in Chapters 2 through 6. Additional topics are covered in the final chapters. The prerequisite is a course covering the basic notions of schemes and sheaves.




Introduction to Singularities


Book Description

This book is an introduction to singularities for graduate students and researchers. Algebraic geometry is said to have originated in the seventeenth century with the famous work Discours de la méthode pour bien conduire sa raison, et chercher la vérité dans les sciences by Descartes. In that book he introduced coordinates to the study of geometry. After its publication, research on algebraic varieties developed steadily. Many beautiful results emerged in mathematicians’ works. First, mostly non-singular varieties were studied. In the past three decades, however, it has become clear that singularities are necessary for us to have a good description of the framework of varieties. For example, it is impossible to formulate minimal model theory for higher-dimensional cases without singularities. A remarkable fact is that the study of singularities is developing and people are beginning to see that singularities are interesting and can be handled by human beings. This book is a handy introduction to singularities for anyone interested in singularities. The focus is on an isolated singularity in an algebraic variety. After preparation of varieties, sheaves, and homological algebra, some known results about 2-dimensional isolated singularities are introduced. Then a classification of higher-dimensional isolated singularities is shown according to plurigenera and the behavior of singularities under a deformation is studied. In the second edition, brief descriptions about recent remarkable developments of the researches are added as the last chapter.




Singularities


Book Description

Publisher Description




American Singularity


Book Description

Since the first shots rang out at Lexington and Concord, signaling the beginning of open war between the colonies and England, America has been credited with a singular conviction, a concern for military veterans' and others' economic and political rights. The idea of America as a promised land of economic opportunity, social mobility, and political freedom has not always flourished. Historians have both given it reality and shaken its substance as they exposed an undercurrent of greed, class conflict, and corruption. In this book Harold Hyman explores the question of American singularity, using the Northwest Ordinance, the Homestead and Morrill acts, and the G.I Bill to measure individual access to land, education, and law. The Northwest Ordinance, enacted in 1787 to encourage settlement of the nation's untamed territories, mandated the establishment of public schools and stable property rights in newly settled lands--specific terms which enshrined the basic liberties secured by the Revolutionary War. Hyman shows that through the Homestead and Morrill acts of 1862, legislators sought to preserve the values of the Union and to prepare for the entrance of the black man into citizenship. Equal access to public lands in the West and to state land-grant universities, countered the economic and social injustices blacks and poor whites would face after the Civil War. Finally, Hyman asserts that the G.I. Bill preserved beneficial social programs forged during the depression, carrying into post-World War II America a widespread concern for education and housing opportunities. Examining the legislation that emerged from three periods of conflict in American history, Hyman reveals a consistent pattern favoring equal access to land, education, and law--a progression of singular, if sometimes flawed, attempts to embody in our statutes the values and aspirations that sparked our major wars.




Singularities Physics Engineering Secohb


Book Description

The book gives a thorough introduction to singularities and their development. It explains in detail important topics such as the types of singularities, their properties, detection and application, and emerging research trends.




Singularities of the Minimal Model Program


Book Description

An authoritative reference and the first comprehensive treatment of the singularities of the minimal model program.




Handbook of Geometry and Topology of Singularities I


Book Description

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject. This is the first volume in a series which aims to provide an accessible account of the state-of-the-art of the subject, its frontiers, and its interactions with other areas of research. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.