Algebraic Geometry in String Theory Seminar

Speaker: Jesse Huang, University of Alberta

Title: Geometric construction of toric NCRs

Abstract: The Rouquier dimension of a toric variety is recently shown to be achieved by the Frobenius pushforward of O via coherent-constructible correspondence. From the perspective of noncommutative geometry, this result leads to a geometric construction of toric NCR of the invariant ring of the Cox ring with respect to a multi-grading which also gives the information about its global dimension. From the perspective of mirror symmetry, the same construction provides a universal “wall skeleton” capturing VGIT wall-crossings, which contains a window for each chamber as a full subcategory. From the perspective of commutative algebra, the same construction indicates the existence of virtual resolutions of the multigraded diagonal bimodule, which agrees with a recent result of Hanlon-Hicks-Larzarev constructing one such resolution explicitly. In this talk, I will survey these perspectives. The talk is based on joint works with P. Zhou, joint works with D. Favero, and work in progress with D. Favero.