Contraction Algebras and Gopakumar--Vafa Invariants

Algebraic Geometry Seminar

Organizers：

Caucher Birkar，贾甲

Speaker：

Hao Zhang (University of Glasgow)

Time：

Fri., 15:30-16:30 , Mar. 20, 2026

Venue：

B725, Shuangqing Complex Building A

Online：

Zoom Meeting ID: 262 865 5007

Passcode: YMSC

Title：

Contraction Algebras and Gopakumar--Vafa Invariants

Abstract:

We study the birational geometry of cAn singularities and their curve-counting invariants via noncommutative methods. Generalised Gopakumar–Vafa invariants are defined for crepant partial resolutions, and Toda’s formula is verified in this setting.

For crepant resolutions, intrinsic Type A potentials on the doubled An quiver classify all crepant resolutions of cAn, confirming the Brown–Wemyss Realisation Conjecture. An explicit example shows that the Donovan–Wemyss Conjecture fails in the non-isolated case.