Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book Arithmetically Cohen-Macaulay Sets of Points in P^1 x P^1 by Elena Guardo, Adam Van Tuyl, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Elena Guardo, Adam Van Tuyl ISBN: 9783319241661
Publisher: Springer International Publishing Publication: November 25, 2015
Imprint: Springer Language: English
Author: Elena Guardo, Adam Van Tuyl
ISBN: 9783319241661
Publisher: Springer International Publishing
Publication: November 25, 2015
Imprint: Springer
Language: English

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.  It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas.  The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points.  The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem.  In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra.  Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research.  Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This brief presents a solution to the interpolation problem for arithmetically Cohen-Macaulay (ACM) sets of points in the multiprojective space P^1 x P^1.  It collects the various current threads in the literature on this topic with the aim of providing a self-contained, unified introduction while also advancing some new ideas.  The relevant constructions related to multiprojective spaces are reviewed first, followed by the basic properties of points in P^1 x P^1, the bigraded Hilbert function, and ACM sets of points.  The authors then show how, using a combinatorial description of ACM points in P^1 x P^1, the bigraded Hilbert function can be computed and, as a result, solve the interpolation problem.  In subsequent chapters, they consider fat points and double points in P^1 x P^1 and demonstrate how to use their results to answer questions and problems of interest in commutative algebra.  Throughout the book, chapters end with a brief historical overview, citations of related results, and, where relevant, open questions that may inspire future research.  Graduate students and researchers working in algebraic geometry and commutative algebra will find this book to be a valuable contribution to the literature.

More books from Springer International Publishing

Cover of the book Advances in Insect Control and Resistance Management by Elena Guardo, Adam Van Tuyl
Cover of the book A Quest Towards a Mathematical Theory of Living Systems by Elena Guardo, Adam Van Tuyl
Cover of the book Pediatric Dermatopathology by Elena Guardo, Adam Van Tuyl
Cover of the book Adapted Compressed Sensing for Effective Hardware Implementations by Elena Guardo, Adam Van Tuyl
Cover of the book Audit Studies: Behind the Scenes with Theory, Method, and Nuance by Elena Guardo, Adam Van Tuyl
Cover of the book Statics of Historic Masonry Constructions by Elena Guardo, Adam Van Tuyl
Cover of the book Reviews of Environmental Contamination and Toxicology Volume 241 by Elena Guardo, Adam Van Tuyl
Cover of the book Progress in Location Based Services 2018 by Elena Guardo, Adam Van Tuyl
Cover of the book Computer Vision for X-Ray Testing by Elena Guardo, Adam Van Tuyl
Cover of the book Marian Devotions, Political Mobilization, and Nationalism in Europe and America by Elena Guardo, Adam Van Tuyl
Cover of the book Stress Echocardiography by Elena Guardo, Adam Van Tuyl
Cover of the book Resisting Neoliberalism in Higher Education Volume I by Elena Guardo, Adam Van Tuyl
Cover of the book Regulation of Ca2+-ATPases,V-ATPases and F-ATPases by Elena Guardo, Adam Van Tuyl
Cover of the book Economy, Finance and Business in Southeastern and Central Europe by Elena Guardo, Adam Van Tuyl
Cover of the book Power Estimation on Electronic System Level using Linear Power Models by Elena Guardo, Adam Van Tuyl
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy