Determinantal Ideals of Square Linear Matrices
يونيو 2024 · Springer Nature
كتاب إلكتروني
318
صفحة
reportلم يتم التحقّق من التقييمات والمراجعات. مزيد من المعلومات
معلومات عن هذا الكتاب الإلكتروني
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.
نبذة عن المؤلف
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.
تقييم هذا الكتاب الإلكتروني
أخبرنا ما هو رأيك.
معلومات القراءة
الهواتف الذكية والأجهزة اللوحية
ينبغي تثبيت تطبيق كتب Google Play لنظام التشغيل Android وiPad/iPhone. يعمل هذا التطبيق على إجراء مزامنة تلقائية مع حسابك ويتيح لك القراءة أثناء الاتصال بالإنترنت أو بلا اتصال بالإنترنت أينما كنت.
أجهزة الكمبيوتر المحمول وأجهزة الكمبيوتر
يمكنك الاستماع إلى الكتب المسموعة التي تم شراؤها على Google Play باستخدام متصفح الويب على جهاز الكمبيوتر.
أجهزة القراءة الإلكترونية والأجهزة الأخرى
للقراءة على أجهزة الحبر الإلكتروني، مثل أجهزة القارئ الإلكتروني Kobo، عليك تنزيل ملف ونقله إلى جهازك. يُرجى اتّباع التعليمات المفصّلة في مركز المساعدة لتتمكّن من نقل الملفات إلى أجهزة القارئ الإلكتروني المتوافقة.
