Abstracts

Tristan Hübsch

Constructing Ricci-flat mirror hypersurfaces within spaces of general type

Complex Ricci-flat (i.e., Calabi-Yau) hypersurfaces in spaces admitting a maximal (toric) U(1)^n gauge symmetry of general type (encoded by certain non-convex and multi-layered multitopes) may degenerate, but can be smoothed by rational (Laurent) anticanonical sections. Nevertheless, the phases of the Gauged Linear Sigma Model and an increasing number of their classical and quantum data are just as computable as for their siblings encoded by reflexive polytopes, and they all have transposition mirror models. Showcasing such hypersurfaces in so-called Hirzebruch scrolls shows this class of constructions to be infinitely vast, yet amenable to several well-founded algebro-geometric methods of analysis. This talk will include joint work with Per Berglund, as reported in part: arXiv:1606.07420, arXiv:1611.10300 and arXiv:2205.12827.