Cox Rings


Book Description

This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.




The Rings of Time


Book Description

When a mining colony on an endangered moon is threatened, it’s a race against time for the Enterprise crew to find a solution in this original novel set in the universe of Star Trek: The Original Series. The USS Enterprise responds to a distress call from a vital dilithium-mining colony in the Klondike system. The colony is located on Skagway, a moon orbiting Klondike-6, a gas giant not unlike Saturn. For unknown reasons, the planet’s rings are coming apart, threatening the colony and its inhabitants. Kirk and his crew need to find a solution—fast.There are more than 3,000 colonists, including hundreds of families, on Skagway, which is more than even the Enterprise can take on, and there are no other rescue ships or habitable planets anywhere in the vicinity. Meanwhile, an approaching comet that may be the source of the crisis turns out to be a mysterious alien probe. Sensors indicate that the probe is incredibly old and running low on power. Suspecting that the probe may have something to do with the threat to Skagway, Kirk has the probe beamed aboard the Enterprise. Suddenly after a blinding flash, Kirk suddenly finds himself floating in orbit above Saturn in our solar system, drifting in space wearing a twenty-first century NASA spacesuit. What just happened?




Cox Rings


Book Description




Arithmetic of Higher-Dimensional Algebraic Varieties


Book Description

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.




Ideals, Varieties, and Algorithms


Book Description

Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.




Using Algebraic Geometry


Book Description

An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.




Combinatorial Algebraic Geometry


Book Description

This volume consolidates selected articles from the 2016 Apprenticeship Program at the Fields Institute, part of the larger program on Combinatorial Algebraic Geometry that ran from July through December of 2016. Written primarily by junior mathematicians, the articles cover a range of topics in combinatorial algebraic geometry including curves, surfaces, Grassmannians, convexity, abelian varieties, and moduli spaces. This book bridges the gap between graduate courses and cutting-edge research by connecting historical sources, computation, explicit examples, and new results.







Theory of Generalized Inverses Over Commutative Rings


Book Description

The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element