A counterexample to the birational Torelli problem for Calabi–Yau threefolds
A counterexample to the birational Torelli problem for Calabi–Yau threefolds
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卡拉比-丘三重的双有理托雷利问题的反例
DOI：
10.1112/jlms.12111
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
J. Rennemo
中科院分区：
文献类型：
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作者：
J. C. Ottem;J. Rennemo
Grassmannian Gr（2，5）通过Plücker嵌入嵌入到P9中。Gr（2，5）的两个广义PGL（10）-平移的交集是一个卡-丘三重X，而两个平移的射影X的交集是另一个卡-丘三重Y，变形等价于X。应用Kuznetsov和Jiang-Leung-Xie的结果，证明了X和Y是等价的，这由阿丁顿的结果暗示了它们的三阶上同调群同构为极化Hodge结构.我们表明，X和Y提供了反例，以一定的'双理性' Torelli声明Calabi-Yau三倍，即，他们是变形等价，派生等价，并同构霍奇结构，但他们不是双理性的。
The Grassmannian Gr (2,5) is embedded in P9 via the Plücker embedding. The intersection of two general PGL(10) ‐translates of Gr (2,5) is a Calabi–Yau threefold X , and the intersection of the projective duals of the two translates is another Calabi–Yau threefold Y , deformation equivalent to X . Applying results of Kuznetsov and Jiang–Leung–Xie shows that X and Y are derived equivalent, which by a result of Addington implies that their third cohomology groups are isomorphic as polarised Hodge structures. We show that X and Y provide counterexamples to a certain ‘birational’ Torelli statement for Calabi–Yau threefolds, namely, they are deformation equivalent, derived equivalent, and have isomorphic Hodge structures, but they are not birational.
K3 表面上扭力轮的模空间和导出的等价物
DOI：
10.1112/jlms/jdw022
发表时间：
2016
期刊：
Journal of the London Mathematical Society
影响因子：
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作者：
Addington N
通讯作者：
Addington N