UID:
almahu_9949773126802882
Format:
XX, 318 p. 5 illus.
,
online resource.
Edition:
1st ed. 2024.
ISBN:
9783031552847
Content:
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.
Note:
Part I: General oversight -- Background steps in determinantal rings -- Algebraic preliminaries -- Geometric oversight -- Part II: Linear section of notable structured square matrices -- Linear sections of the generic square matrix -- Symmetry preserving linear sections of the generic symmetric matrix -- Linear sections of the generic square Hankel matrix -- Hankel like catalecticants -- The dual variety of a linear determinantal hypersurface -- Part III: Other classes of linear sections -- Hilbert-Burch linear sections -- Apocryphal classes -- Appendix -- Index.
In:
Springer Nature eBook
Additional Edition:
Printed edition: ISBN 9783031552830
Additional Edition:
Printed edition: ISBN 9783031552854
Additional Edition:
Printed edition: ISBN 9783031559464
Language:
English
DOI:
10.1007/978-3-031-55284-7
URL:
https://doi.org/10.1007/978-3-031-55284-7
URL:
Volltext
(URL des Erstveröffentlichers)
