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020 _a9783031552847
_9978-3-031-55284-7
024 7 _a10.1007/978-3-031-55284-7
_2doi
050 4 _aQA251.3
072 7 _aPBF
_2bicssc
072 7 _aMAT002010
_2bisacsh
072 7 _aPBF
_2thema
100 1 _aRamos, Zaqueu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978163
245 1 0 _aDeterminantal Ideals of Square Linear Matrices
_h[electronic resource] /
_cby Zaqueu Ramos, Aron Simis.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXX, 318 p. 5 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _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.
520 _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.
650 0 _aCommutative algebra.
_970151
650 0 _aCommutative rings.
_970152
650 0 _aAlgebraic geometry.
650 0 _aAlgebraic fields.
_970148
650 0 _aPolynomials.
_964269
650 1 4 _aCommutative Rings and Algebras.
_970156
650 2 4 _aAlgebraic Geometry.
650 2 4 _aField Theory and Polynomials.
_970153
700 1 _aSimis, Aron.
_eauthor.
_0(orcid)0000-0002-2848-8509
_1https://orcid.org/0000-0002-2848-8509
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978164
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031552830
776 0 8 _iPrinted edition:
_z9783031552854
776 0 8 _iPrinted edition:
_z9783031559464
856 4 0 _uhttps://doi.org/10.1007/978-3-031-55284-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60476
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