Stability, duality, and DT invariants for flopping curves

Abstract: Threefold flops are birational surgeries on a contractible curve that connect minimal models of threefolds, and are therefore crucial to the minimal model program. To examine these flops one would like to compute their Donaldson-Thomas invariants, which are virtual counts of semistable objects in the derived category. In this talk I will explain how to determine the semistable objects supported on a flopping curve by showing that their K-theory classes are dual to a hyperplane arrangement induced by tilting complexes. I will also show how this duality can be categorified to give a full description of the (3-Calabi-Yau) deformation theory of these objects, which has various implications for the DT theory.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

Comments: https://us02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

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