Harvard-MIT Algebraic Geometry Seminar: CM-minimizers and standard models of Fano fibrations over curves


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February 27, 2024 3:00 pm - 4:00 pm
MIT, Room 2-132

Maksym Fedorchuk - Boston College

A recent achievement in K-stability of Fano varieties is an algebro-geometric construction of a projective moduli space of K-polystable Fanos. The ample line bundle on this moduli space is the CM line bundle of Tian. One of the consequences of the general theory is that given a family of K-stable Fanos over a punctured curve, the polystable filling is the one that minimizes the degree of the CM line bundle after every finite base change. A natural question is to ask what are the CM-minimizers without base change. In answering this question, we arrive at a theory of Kollár stability for fibrations over one-dimensional bases, and standard models of Fano fibrations. After explaining the general theory, I will sketch work in progress on standard models of quartic threefold hypersurfaces. This talk is based on joint work with Hamid Abban and Igor Krylov.

For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar