From real affine geometry to complex geometry
From real affine geometry to complex geometry
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从真正的仿射几何到复杂几何
DOI：
10.4007/annals.2011.174.3.1
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发表时间：
2007
影响因子：
4.9
通讯作者：
Bernd S Siebert
中科院分区：
文献类型：
--
作者：
M. Gross;Bernd S Siebert
我们从具有奇点的实流形(热带流形)构造了Calabi-Yau流形的退化。这解决了镜像对称性中的一个基本问题。此外，我们的方法的一个显著特点是，它产生了热带树族退化的显式和规范的逐级描述。这就完全控制了在热带几何条件下镜面对称性的B模侧。例如，我们期望我们的形变参数是标准坐标，并且期望周期计算可以用热带曲线来表示。我们预计这将导致通过热带方法证明镜像对称性。
We construct from a real ane manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical order-by-order description of the degeneration via families of tropical trees. This gives complete control of the B-model side of mirror symmetry in terms of tropical geometry. For example, we expect that our deformation parameter is a canonical coordinate, and expect period calculations to be expressible in terms of tropical curves. We anticipate this will lead to a proof of mirror symmetry via tropical methods.