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Brown, Gavin and Wemyss, Michael (2018) Gopakumar--Vafa invariants do not determine flops. Communications in Mathematical Physics, 361 (1). pp. 143-154. doi:10.1007/s00220-017-3038-z ISSN 0010-3616.
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Official URL: https://doi.org/10.1007/s00220-017-3038-z
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: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Geometry, Algebraic, Algebra, Homological, Isomorphisms (Mathematics) | ||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0010-3616 | ||||||||
| Official Date: | 31 July 2018 | ||||||||
| Dates: |
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| Volume: | 361 | ||||||||
| Number: | 1 | ||||||||
| Page Range: | pp. 143-154 | ||||||||
| DOI: | 10.1007/s00220-017-3038-z | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 23 October 2017 | ||||||||
| Date of first compliant Open Access: | 12 February 2018 | ||||||||
| RIOXX Funder/Project Grant: |
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