2024/12/12 by Alexandra Seceleanu, Seceleanu, Alexandra
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Analytic and geometric function theory
paper · pdf · doi:10.48550/arxiv.2412.08917
These lecture notes were prepared for the Lefschetz Preparatory School, a graduate summer course held in Krakow, May 6-10, 2024. They present the story of the algebraic Lefschetz properties from their origin in algebraic geometry to some recent developments in commutative algebra. The common thread of the notes is a bias towards topics surrounding the algebraic Lefschetz properties that have a topological flavor. These range from the Hard Lefschetz Theorem for cohomology rings to commutative algebraic analogues of these rings, namely artinian Gorenstein rings, and topologically motivated operations among such rings.