Derived autoequivalences of length 2 flops via GIT

2025/08/07 by Varshney, Aporva
#18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.05285

Abstract

We obtain the derived autoequivalences of a flopping rational curve of length 2 using GIT and the theory of windows applied to the universal length 2 flop. We show that the stringy Kähler moduli space (SKMS) associated to the GIT problem, as constructed by Halpern-Leistner-Sam, matches the description of the space obtained for length 2 threefolds by Hirano-Wemyss as a quotient of a Bridgeland stability manifold. Furthermore, we show that its fundamental group acts via contraction algebra and fibre algebra twists, hence recovering the monodromy action described by Donovan-Wemyss. In particular, this shows that the two approaches to building the SKMS agree in this setting.

Citations

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Related

• Donaldson-Thomas invariants of length 2 flops
• Stringy Kähler moduli, mutation and monodromy
• Autoequivalences for 3-fold flops: an overview
• Stability Conditions for 3-fold Flops
• The length classification of threefold flops via noncommutative algebras