Gopakumar-Vafa Invariants Do Not Determine Flops
Gopakumar-Vafa Invariants Do Not Determine Flops
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Gopakumar-Vafa 不变量不决定失败次数
DOI：
10.1007/s00220-017-3038-z
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发表时间：
2017
影响因子：
2.4
通讯作者：
Brown G
中科院分区：
文献类型：
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作者：
Brown G
展示了两个3倍翻转，两者都恰好具有一个翻转曲线。这两个触发器之一是新的，是不同于所有已知的algebraicD 4触发器。它表明，这两个触发器既不是代数同构，也不是解析同构，但他们的曲线计数Gopakumar-Vafa不变量是相同的。我们进一步表明，与两者相关的收缩代数是不同构的，所以在这个水平上的触发器是区分。这表明，压缩代数是一个更精细的不变量比各种曲线计数理论，它也提供了更多的证据，建议的分析分类的3倍触发器通过压缩代数。
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 algebraicD4-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.