Titlebook: Recent Developments in Commutative Algebra; Levico Terme, Trento Claudia Polini,Claudiu Raicu,Mark E. Walker,Aldo C Book 2021 The Editor(s)

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elopment Dr. Rabinovich was able to complete very recently. This method, which is called the Method of Enumeration, produces estimates that are no longer approximate, similar to the way the method of reduction described in the first edition removed approximation in estimating uncertainty of indirect

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Matteo Varbaroe measurement accuracy and recommendations on how to calculate systematic error of multiple measurements. There is also an extended section on the method of reduction, which provides an alternative to the least-square method and the method of enumeration. Many sections are also rewritten to improve

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Koszul Modules,ing recent work of Aprodu, Farkas, Papadima, Raicu, and Weyman (Invent. Math. .(3), 657–720 (2019)). More precisely, we discuss a relationship between Koszul modules and the syzygies of the tangent developable surface to a rational normal curve, which arises from a version of Hermite reciprocity for

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,Gröbner Degenerations,the recent result achieved in (Conca and Varbaro, Invent. math. .(3), 713–730 (2020)) that, if a homogeneous polynomial ideal admits a squarefree monomial initial ideal, then the local cohomology modules of the original ideal and those of such initial ideal have the same Hilbert functions.

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0075-8434 ume, based on lectures given at a workshop held in Levico Terme, Trento, in July 2019, highlights some of these developments. The text will be a valuable asset to graduate students and researchers in commutative algebra and related fields..978-3-030-65063-6978-3-030-65064-3Series ISSN 0075-8434 Series E-ISSN 1617-9692

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Defining Equations of Blowup Algebras,ommutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps. In these lectures we will discuss this topic in several situations.