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Quasi-universal sheaves and generic bricks

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EMGW02 - Applied and computational algebraic geometry

This is based on joint work-in-progress with Colin Ingalls and Charles Paquette. Given a finite-dimensional algebra, we can associate a quiver and choose a dimension vector. Work of Alistair King shows that, if the dimension vector is unimodular, there is a moduli space of stable representations with a universal sheaf. Work of Reineke–Schröer and Hoskins–Schaffhauser shows that this does not hold for all dimension vectors; in general, we obtain only a “quasi-universal sheaf”. I will discuss this construction from several perspectives, and explain applications to the representation theory of finite-dimensional algebras.

This talk is part of the Isaac Newton Institute Seminar Series series.

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