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Martí Salat: Multigraded Hilbert function for modules over the Cox ring of a toric variety

Tid: Må 2021-11-08 kl 15.00 - 16.00

Plats: Zoom, meeting ID: 619 3088 8063

Föreläsare: Martí Salat (University of Barcelona)

Abstract

In this talk, we consider \(\mathbb{Z}^r\)−graded modules on the \(\operatorname{Cl}(X)\)−graded Cox ring \(k[x_1,\dots,x_r]\) of a smooth complete toric variety \(X\). Using the theory of Klyachko filtrations in the reflexive case, we construct a collection of lattice polytopes codifying the multigraded Hilbert function of the module. We apply this approach to reflexive \(\mathbb{Z}^{s+r+2}\)−graded modules over any non-standard bigraded polynomial ring \(k[x_0,\dots,x_s, y_0,\dots,y_r]\). In this case, we give sharp bounds for the multigraded regularity index of their multigraded Hilbert function, and a method to compute their Hilbert polynomial.