04145nam a22005535i 4500 978-3-031-55284-7 DE-He213 20251030112255.0 cr nn 008mamaa 240603s2024 sz | s |||| 0|eng d 9783031552847 978-3-031-55284-7 10.1007/978-3-031-55284-7 doi QA251.3 PBF bicssc MAT002010 bisacsh PBF thema Ramos, Zaqueu. author. aut http://id.loc.gov/vocabulary/relators/aut 78163 Determinantal Ideals of Square Linear Matrices [electronic resource] / by Zaqueu Ramos, Aron Simis. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XX, 318 p. 5 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda 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. 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. Commutative algebra. 70151 Commutative rings. 70152 Algebraic geometry. Algebraic fields. 70148 Polynomials. 64269 Commutative Rings and Algebras. 70156 Algebraic Geometry. Field Theory and Polynomials. 70153 Simis, Aron. author. (orcid)0000-0002-2848-8509 https://orcid.org/0000-0002-2848-8509 aut http://id.loc.gov/vocabulary/relators/aut 78164 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031552830 Printed edition: 9783031552854 Printed edition: 9783031559464 https://doi.org/10.1007/978-3-031-55284-7 ZDB-2-SMA ZDB-2-SXMS 60476 60476