Tropically constructed Lagrangians in mirror quintic threefolds
Tropically constructed Lagrangians in mirror quintic threefolds
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镜像五次三重中热带构造的拉格朗日量
DOI：
10.1017/fms.2020.54
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Helge Ruddat
中科院分区：
文献类型：
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作者：
C. Mak;Helge Ruddat
摘要利用热带曲线和复曲面退化技术，构造了大量的Calabi-Yau三重闭嵌入拉格朗日有理同调球面。同调球是全纯曲线的镜像对偶，对Gromov-Witten（GW）不变量有贡献。根据Joyce的猜想，这些拉格朗日量被期望具有特殊的拉格朗日量代表，从而解决卡-丘三重中的特殊拉格朗日计数问题。我们将这种构造应用于从五次卡-丘三重上的2，875条线获得的热带曲线。每个容许的热带曲线给出了相应的镜像五次三倍的拉格朗日有理同调球，这些拉格朗日函数的乔伊斯权重等于相应的热带曲线的多重性。作为应用，我们证明了不相交曲线给出了两两同调但非哈密顿的同位素拉格朗日量，并且我们在一个例子中检查，
$>300$
相互不相交的曲线（因此拉格朗日）出现。德恩扭转沿着这些拉格朗日生成一个交换子群的辛映射类组的秩。
Abstract We use tropical curves and toric degeneration techniques to construct closed embedded Lagrangian rational homology spheres in a lot of Calabi-Yau threefolds. The homology spheres are mirror dual to the holomorphic curves contributing to the Gromov-Witten (GW) invariants. In view of Joyce’s conjecture, these Lagrangians are expected to have special Lagrangian representatives and hence solve a special Lagrangian enumerative problem in Calabi-Yau threefolds. We apply this construction to the tropical curves obtained from the 2,875 lines on the quintic Calabi-Yau threefold. Each admissible tropical curve gives a Lagrangian rational homology sphere in the corresponding mirror quintic threefold and the Joyce’s weight of each of these Lagrangians equals the multiplicity of the corresponding tropical curve. As applications, we show that disjoint curves give pairwise homologous but non-Hamiltonian isotopic Lagrangians and we check in an example that
$>300$
mutually disjoint curves (and hence Lagrangians) arise. Dehn twists along these Lagrangians generate an abelian subgroup of the symplectic mapping class group with that rank.
构建拉格朗日环面纤维局部模型
影响因子：
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作者：
Evans J
通讯作者：
Evans J