Contraction algebra and invariants of singularities

2016/01/19 by Zheng Hua, Hua, Zheng, Yukinobu Toda +1 · 1 citation
Mathematics · Physics and Astronomy · #14E30 #14N35 #16S38 #18E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1601.04881

openalex publication_date 2016/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [7], Donovan and Wemyss introduced the contraction algebra of flop- ping curves in 3-folds. When the flopping curve is smooth and irreducible, we prove that the contraction algebra together with its A_∞-structure recovers various invariants associated to the underlying singularity and its small resolution, including the derived category of singularities and the genus zero Gopakuma-Vafa invariants.

Citations

• Maximal Modifications and Auslander-Reiten Duality for Non-isolated Singularities
• Non-commutative width and Gopakumar-Vafa invariants

Cited by

• On constructing deformations of noncommutative algebras

Related

• Contractions of 3-folds: deformations and invariants
• The derived contraction algebra
• Flops, Type III contractions and Gromov-Witten invariants on Calabi-Yau threefolds
• Noncommutative Singularity Theory
• Genus zero Gopakumar-Vafa invariants of contractible curves