Refined Harder-Narasimhan filtrations in moduli theory

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• Andrés Ibáñez Núñez
• Wednesday 17 January 2024, 14:15-15:15
• CMS MR13.

If you have a question about this talk, please contact Dhruv Ranganathan.

We introduce a notion of refined Harder-Narasimhan filtration, defined abstractly for algebraic stacks satisfying natural conditions. Examples include moduli stacks of objects at the heart of a Bridgeland stability condition, moduli stacks of K-semistable Fano varieties, moduli of principal bundles on a curve, and quotient stacks. We will explain how refined Harder-Narasimhan filtrations are closely related both to stratifications and to the asymptotics of certain analytic flows, relating and expanding work of Kirwan and Haiden-Katzarkov-Kontsevich-Pandit, respectively. In the case of quotient stacks by the action of a torus, the refined Harder-Narasimhan filtration can be computed in terms of convex geometry.

This talk is part of the Algebraic Geometry Seminar series.

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