Systoles, Special Lagrangians, and Bridgeland stability conditions
Systoles, Special Lagrangians, and Bridgeland stability conditions
复制标题
收缩、特殊拉格朗日和布里奇兰稳定性条件
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Yu
中科院分区：
文献类型：
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作者：
Yu
受Loewner环面不等式的启发，该不等式将环面上的不可收缩环（收缩）的最小长度与其体积联系起来，人们可以问是否存在更高维的类似物，其中环面被Calabi-Yau流形取代，环被特殊的拉格朗日子流形取代。
我们试图回答这个问题的情况下，镜像四次K3曲面通过镜像对称性和Bridgeland稳定性条件。我们定义了范畴收缩和收缩比的Bridgeland稳定性条件的概念，并表明，上述问题是一个纯粹的格理论问题。我们证明了格理论问题的答案是有限的，并给出了一个明确的上界。计算出精确的答案会很有趣。
Motivated by Loewner's torus inequality which relates the least length of a non-contractible loop (systole) on a torus to its volume, one can ask whether there is a higher-dimensional analogue, with torus replaced by Calabi-Yau manifolds and loops replaced by special Lagrangian submanifolds.
We attempt to answer this question in the case of mirror quartic K3 surfaces via mirror symmetry and Bridgeland stability conditions. We define the notion of categorical systole and systolic ratio of a Bridgeland stability condition, and show that the aforementioned question is related to a purely lattice-theoretic problem. We prove that the answer to the lattice-theoretic problem is finite and give an explicit upper bound. It would be interesting to compute the precise answer.
影响因子：
6.2
作者：
Bridgeland, Tom;Smith, Ivan
通讯作者：
Smith, Ivan