03772nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001200153072001600165072002300181072001500204100007600219245010600295250001800401264007500419300004200494336002600536337002600562338003600588347002400624505057400648520152001222650002502742650002302767650002402790650002202814650001702836650003602853650002402889650003402913700014102947710003403088773002603122776003603148776003603184776003603220856004603256978-3-031-55284-7DE-He21320251030112255.0cr nn 008mamaa240603s2024    sz |    s    |||| 0|eng d  a97830315528477 a10.1007/978-3-031-55284-72doi 4aQA251.3 7aPBF2bicssc 7aMAT0020102bisacsh 7aPBF2thema1 aRamos, Zaqueu.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aDeterminantal Ideals of Square Linear Matricesh[electronic resource] /cby Zaqueu Ramos, Aron Simis.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXX, 318 p. 5 illus.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda0 aPart 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.  aThis 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. 0aCommutative algebra. 0aCommutative rings. 0aAlgebraic geometry. 0aAlgebraic fields. 0aPolynomials.14aCommutative Rings and Algebras.24aAlgebraic Geometry.24aField Theory and Polynomials.1 aSimis, Aron.eauthor.0(orcid)0000-0002-2848-85091https://orcid.org/0000-0002-2848-85094aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303155283008iPrinted edition:z978303155285408iPrinted edition:z978303155946440uhttps://doi.org/10.1007/978-3-031-55284-7