Refined Donaldson-Thomas theory of threefold flops

Okke van Garderen (Glasgow)

26-Nov-2020, 13:30-14:30 (3 years ago)

Abstract: DT invariants are virtual counts of semistable objects in the derived category of a Calabi-Yau variety, which can be calculated at various levels of refinement. An interesting family of CY variety which are of particular interest to the MMP are threefold flopping curves, and in this talk I will explain how to understand their DT theory. The key point is that the stability conditions on the derived categories can be understood via tilting equivalences, which can be seen as the analogue of cluster mutations in this setting. I will show that these equivalences induce wall-crossing formulas, and use this to reduce the DT theory of a flop to a comprehensible set of curve-counting invariants, which can be computed for several examples. These computations produce new evidence for a conjecture of Pandharipande-Thomas, and show that refined DT invariants are not enough to completely classify flops.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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