关于此电子书
This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices. Its content has been extensively tested in several lectures given on various occasions, typically to audiences composed of commutative algebraists, algebraic geometers, and singularity theorists.
Traditionally, texts on this topic showcase determinantal rings as the main actors, emphasizing their properties as algebras. This book follows a different path, exploring the role of the ideal theory of minors in various situations—highlighting the use of Fitting ideals, for example. Topics include an introduction to the subject, explaining matrices and their ideals of minors, as well as classical and recent bounds for codimension. This is followed by examples of algebraic varieties defined by such ideals. The book also explores properties of matrices that impact their ideals of minors, such as the 1-generic property, explicitly presenting a criterion by Eisenbud. Additionally, the authors address the problem of the degeneration of generic matrices and their ideals of minors, along with applications to the dual varieties of some of the ideals.
Primarily intended for graduate students and scholars in the areas of commutative algebra, algebraic geometry, and singularity theory, the book can also be used in advanced seminars and as a source of aid. It is suitable for beginner graduate students who have completed a first course in commutative algebra.
Traditionally, texts on this topic showcase determinantal rings as the main actors, emphasizing their properties as algebras. This book follows a different path, exploring the role of the ideal theory of minors in various situations—highlighting the use of Fitting ideals, for example. Topics include an introduction to the subject, explaining matrices and their ideals of minors, as well as classical and recent bounds for codimension. This is followed by examples of algebraic varieties defined by such ideals. The book also explores properties of matrices that impact their ideals of minors, such as the 1-generic property, explicitly presenting a criterion by Eisenbud. Additionally, the authors address the problem of the degeneration of generic matrices and their ideals of minors, along with applications to the dual varieties of some of the ideals.
Primarily intended for graduate students and scholars in the areas of commutative algebra, algebraic geometry, and singularity theory, the book can also be used in advanced seminars and as a source of aid. It is suitable for beginner graduate students who have completed a first course in commutative algebra.
作者简介
Zaqueu Ramos is a Professor at the Federal University of Sergipe, Brazil. He holds a bachelor's degree in Mathematics from the Federal University of Sergipe, Brazil and a PhD degree in Mathematics from the Federal University of Pernambuco (2012). He completed his postdoctorate studies at the Federal University of Paraíba (2014-2015) under the supervision of Aron Simis. His research focuses on commutative algebra and its interactions with algebraic geometry.
Aron Simis is an Emeritus Full Professor at the Federal University of Pernambuco, Brazil. He earned his PhD from Queen's University, Canada, under the supervision of Paulo Ribenboim. He previously held a full professorship at IMPA, Rio de Janeiro, Brazil. He was President of the Brazilian Mathematical Society (1985-1987) and a member, on several occasions, of international commissions of the IMU (International Mathematical Union) and TWAS (Academy of Sciences for the Developing World). His main research interests include main structures in commutative algebra; projective varieties in algebraic geometry; aspects of algebraic combinatorics; special graded algebras; foundations of Rees algebras; cremona and birational maps; algebraic vector fields; and differential methods.
Aron Simis is an Emeritus Full Professor at the Federal University of Pernambuco, Brazil. He earned his PhD from Queen's University, Canada, under the supervision of Paulo Ribenboim. He previously held a full professorship at IMPA, Rio de Janeiro, Brazil. He was President of the Brazilian Mathematical Society (1985-1987) and a member, on several occasions, of international commissions of the IMU (International Mathematical Union) and TWAS (Academy of Sciences for the Developing World). His main research interests include main structures in commutative algebra; projective varieties in algebraic geometry; aspects of algebraic combinatorics; special graded algebras; foundations of Rees algebras; cremona and birational maps; algebraic vector fields; and differential methods.
为此电子书评分
欢迎向我们提供反馈意见。
如何阅读
智能手机和平板电脑
笔记本电脑和台式机
您可以使用计算机的网络浏览器聆听您在 Google Play 购买的有声读物。
电子阅读器和其他设备
如果要在 Kobo 电子阅读器等电子墨水屏设备上阅读，您需要下载一个文件，并将其传输到相应设备上。若要将文件传输到受支持的电子阅读器上，请按帮助中心内的详细说明操作。
