Gopakumar--Vafa invariants do not determine flops

Brown, G. and Wemyss, M. (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361(1), pp. 143-154. (doi:10.1007/s00220-017-3038-z)

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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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Brown, G., and Wemyss, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Communications in Mathematical Physics
Publisher:Springer
ISSN:0010-3616
ISSN (Online):1432-0916
Published Online:16 November 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Communications in Mathematical Physics 361(1):143-154
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
756641The Homological Minimal Model ProgramMichael WemyssEngineering and Physical Sciences Research Council (EPSRC)EP/K021400/2M&S - MATHEMATICS