Calabi–Yau threefolds with a curve of singularities and counterexamples to the Torelli problem II
Calabi–Yau threefolds with a curve of singularities and counterexamples to the Torelli problem II
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卡拉比-丘三重与奇点曲线和托雷利问题 II 的反例
DOI：
10.1017/s0305004100004588
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发表时间：
1999
影响因子：
0.8
通讯作者：
Balázs Szendrői
中科院分区：
文献类型：
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作者：
Balázs Szendrői
本文是[15]的继续。在这篇论文中，我介绍了一个一般框架，它允许一个生产'弱'反例托雷利卡-丘三倍：变形家庭包含非同构品种Y t，Y+t同构霍奇理论的第三上同调。这些变种是作为三重Y的变形而出现的，这些变形是奇异变种X的分解，具有相当特殊的性质（参见。第1节）。在[15]中，我讨论了包含合适的X的两个族，它们确实提供了一个反例，而第三个族具有非常相似的性质，但是非平凡的一般自同构的存在破坏了反例。这表明明确的例子是必要的;为了得到Torelli（定理1·1）的反例，需要仔细检查一组精确的条件。事实上，存在着几个族的自同构（注4·5）。
This paper is a continuation of [15]. In that paper, I introduced a general framework which allows one to produce ‘weak’ counterexamples to Torelli for Calabi–Yau threefolds: deformation families containing non-isomorphic varieties Yt, Y+t with isomorphic Hodge theory on the third cohomology. The varieties arise as deformations of threefolds Y that are resolutions of singular varieties X with rather special properties (cf. Section 1). In [15], I discussed two families containing suitable X that do provide a counterexample and a third family with remarkably similar properties where however the existence of a nontrivial generic automorphism destroys the counterexample. This shows that explicit examples are necessary; there is a precise set of conditions one needs to check carefully in order to obtain counterexamples to Torelli (Theorem 1·1). In fact, there exist several families with renitent automorphisms (Remark 4·5).
DOI：
10.1090/s0894-0347-1992-1149195-9
发表时间：
1992-09
影响因子：
3.9
作者：
J. Kollár;S. Mori
通讯作者：
J. Kollár;S. Mori