Titlebook: Commutative Algebra; Expository Papers De Irena Peeva Book 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to

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Algebraic Geometry, Commutative Algebra and Combinatorics: Interactions and Open Problems,f semi-effectivity, the second part is on the containment problem of symbolic powers of ideals of fat points in their ordinary powers, and the third part is on splitting types of rank 2 bundles on rational curves.

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eld.Is accessible to graduate students and researchers who a.This contributed volume is a follow-up to the 2013 volume of the same title, published in honor of noted Algebraist David Eisenbud‘s 65th birthday. It brings together the highest quality expository papers written by leaders and talented ju

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The Simplest Minimal Free Resolutions in ,,sbaum-Eisenbud criteria for exactness, Hilbert-Burch theorem), and homological algebra (Koszul homology, spectral sequences). We treat in detail the case in which the bidegree is (1, .). We connect our work to a conjecture of Fr?berg–Lundqvist on bigraded Hilbert functions, and close with a number of open problems.

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Subadditivity of Syzygies of Ideals and Related Problems,partial information about the beginning of a free resolution, such as degrees of generators or degrees of first syzygies. We also focus specifically on conditions that guarantee an ideal is quadratic with linear resolution for a fixed number of steps. Finally we collect some old and new open problems on degrees of syzygies.

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Applications of Liaison,urry of new insights and applications. After reviewing some needed concepts and results, several of these applications are discussed. Topics include Hilbert functions and free resolutions, hyperplane arrangements, Gr?bner bases, Rees algebras, simplicial complexes and more.