Titlebook: Determinants, Gröbner Bases and Cohomology; Winfried Bruns,Aldo Conca,Matteo Varbaro Book 2022 Springer Nature Switzerland AG 2022 Determi

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Algebras Defined by Minors,rated by minors through their initial algebras. Since the initial algebras are normal monoid domains, toric algebra can be applied to them. Since normal monoid domains are very well understood, we can draw strong consequences for the algebras defined by minors.

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Book 2022h tools from combinatorics, algebra, representation theory and geometry..After a concise introduction to Gröbner and Sagbi bases, determinantal ideals are studied via the standard monomial theory and the straightening law. This opens the door for representation theoretic methods, such as the Robinso

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The Impact on Major Industries, to the rationality of singularities in characteristic 0, so that we can at least briefly discuss this property for determinantal rings. F-rationality is a very handy tool for the exploitation of toric and equivariant deformations.

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Asymptotic Regularity for Symbolic Powers of Determinantal Ideals, the asymptotic regularity. We end Chapter 10 with a brief survey of several other homological and arithmetic properties of determinantal ideals that can be derived in a compact way via geometric arguments.

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,Cohomology and Regularity in Characteristic Zero,ion of the calculation of Ext modules, we explain how to describe the GL-structure for the local cohomology with support in determinantal ideals. Finally, we conclude the book with a quick survey of the important topic of free resolutions of determinantal ideals.

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