Gopakumar-Vafa invariants do not determine flops

Abstract

Two 3-fold flops are exhibited, both of which have precisely one flopping curve. One of the two flops is new, and is distinct from all known algebraic D4-flops. It is shown that the two flops are neither algebraically nor analytically isomorphic, yet their curve-counting Gopakumar-Vafa invariants are the same. We further show that the contraction algebras associated to both are not isomorphic, so the flops are distinguished at this level. This shows that the contraction algebra is a finer invariant than various curve-counting theories, and it also provides more evidence for the proposed analytic classification of 3-fold flops via contraction algebras.

10 pages, final version

References in corpus (3)

• Noncommutative deformations and flops
• 13/2 ways of counting curves
• Quivers from Matrix Factorizations

Cited by in corpus (6)

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• Genus zero Gopakumar-Vafa invariants from open strings
• 5d Higgs Branches from M-theory on quasi-homogeneous cDV threefold singularities
• On the Finiteness of the Derived Equivalence Classes of some Stable Endomorphism Rings
• Flops of any length, Gopakumar-Vafa invariants, and 5d Higgs Branches
• Local Normal Forms of Noncommutative Functions