Aaron Bertram (Utah)

Title: Stability and Regularity

Abstract: In this talk, I want to relate the graded syzygies of a coherent sheaf on projective space with a family of "Euler" stability conditions. I am promoting a point of view: graded syzygies (especially the minimal free resolution) should be organized into filtrations, which will often be Harder-Narasimhan filtrations for appropriate stability conditions. The picture that emerges is a series of moduli spaces, each constructed by Geometric Invariant Theory, that culminates in the moduli space of Gieseker-stable sheaves.

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