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This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Gröbner bases and degenerations, and applications of Adams operations. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of long-standing problems; the new techniques and perspectives are leading to an extraordinary transformation in the field. The material contained in this volume, 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.

Commutative algebra. --- Commutative rings. --- Algebraic geometry. --- Commutative Rings and Algebras. --- Algebraic Geometry. --- Algebraic geometry --- Geometry --- Rings (Algebra) --- Algebra --- Geometry, Algebraic. --- Àlgebra commutativa --- Geometria algebraica --- Geometria algèbrica --- Geometria --- Anàlisi p-àdica --- Cicles algebraics --- Espais algebraics --- Esquemes (Geometria algebraica) --- Esquemes de grups (Matemàtica) --- Geometria algebraica aritmètica --- Grups algebraics lineals --- Geometria analítica --- Geometria biracional --- Geometria enumerativa --- Geometria tropical --- Homologia --- Singularitats (Matemàtica) --- Superfícies algebraiques --- Teoria de mòduls --- Teoria de la intersecció --- Teoria de Hodge --- Varietats abelianes --- Varietats algebraiques --- Corbes algebraiques --- Funcions abelianes --- Àlgebres commutatives --- Àlgebra --- Teoria de la dimensió (Àlgebra)

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Ordered algebraic structures --- Geometry --- algebra --- landmeetkunde