Star configurations and symmetric shifted ideals

Abstract: The ideals of so-called star configurations have been studied in connection to commutative algebra and combinatorics. The problem of describing the Betti numbers of the symbolic powers of these ideals was recently settled. I will present a solution to this problem obtained in joint work with Biermann, De Alba, Murai, Nagel, O’Keefe, R ̈omer, and Seceleanu. Our results rely on the natural action of a symmetric group to study a larger class of ideals that we call ’symmetric shifted ideals’.

commutative algebraalgebraic geometrycombinatoricsrings and algebrasrepresentation theory

Audience: researchers in the topic

Geometry, Algebra, Singularities, and Combinatorics

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