Current and New Directions Nagel, Uwe. editor. edt http://id.loc.gov/vocabulary/relators/edt Adiprasito, Karim. editor. edt http://id.loc.gov/vocabulary/relators/edt Di Gennaro, Roberta. editor. edt http://id.loc.gov/vocabulary/relators/edt Faridi, Sara. editor. edt http://id.loc.gov/vocabulary/relators/edt Murai, Satoshi. editor. edt http://id.loc.gov/vocabulary/relators/edt SpringerLink (Online service) text si 2024 1st ed. 2024. monographic eng

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access X, 225 p. 19 illus., 1 illus. in color. online resource. The study of Lefschetz properties for Artinian algebras was motivated by the Lefschetz theory for projective manifolds. Recent developments have demonstrated important cases of the Lefschetz property beyond the original geometric settings, such as Coxeter groups or matroids. Furthermore, there are connections to other branches of mathematics, for example, commutative algebra, algebraic topology, and combinatorics. Important results in this area have been obtained by finding unexpected connections between apparently different topics. A conference in Cortona, Italy in September 2022 brought together researchers discussing recent developments and working on new problems related to the Lefschetz properties. The book will feature surveys on several aspects of the theory as well as articles on new results and open problems. Survey articles about specific topics -- Jordan types and relation with WLP/SLP -- Unexpected objects, connections with Lefschetz properties and special sets of points -- Combinatorial aspects -- Working group on Perazzo hypersurfaces Hilbert functions, WLP, Jordan types. edited by Uwe Nagel, Karim Adiprasito, Roberta Di Gennaro, Sara Faridi, Satoshi Murai. Algebraic topology Algebraic Topology QA612-612.8 9789819738861 https://doi.org/10.1007/978-981-97-3886-1 https://doi.org/10.1007/978-981-97-3886-1 240831 20251030112926.0 978-981-97-3886-1