Moduli of Representations, Quiver Grassmannians, and Hilbert Schemes

2015/05/22 by Lutz Hille, Hille, Lutz
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.1505.06008

8 pages, 2 figures

arxiv created 2015/05/22 · arxiv updated 2015/05/25

Abstract

It is a well established fact, that any projective algebraic variety is a moduli space of representations over some finite dimensional algebra. This algebra can be chosen in several ways. The counterpart in algebraic geometry is tautological: every variety is its own Hilber scheme of sheaves of length one. This holds even scheme theoretic. We use Beilinson's equivalence to get similar results for finite dimensional algebras, including moduli spaces and quiver grassmannians. Moreover, we show that several already known results can be traced back to the Hilbert scheme construction and Beilinson's equivalence.

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