Derived Theta-stratifications and the D-equivalence conjecture

Abstract: Every vector bundle on a smooth curve has a canonical filtration, called the Harder-Narasimhan filtration, and the moduli of all vector bundles admits a stratification based on the properties of the Harder-Narasimhan filtration at each point. The theory of Theta-stratifications formulates this structure on a general algebraic stack. I will discuss how to characterize stratifications of this kind, and why their local cohomology is particularly well-behaved. I will then explain how Theta-stratifications are part of a recent proof of a case of the D-equivalence conjecture: for any projective Calabi-Yau manifold X that is birationally equivalent to a moduli space of semistable coherent sheaves on a K3 surface, the derived category of coherent sheaves on X is equivalent to the derived category of this moduli space. This confirms a prediction from homological mirror symmetry for this class of compact Calabi-Yau manifold

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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