论文标题
一类Calabi-yau Hypersurfaces
Tropical and non-Archimedean Monge-Ampère equations for a class of Calabi-Yau hypersurfaces
论文作者
论文摘要
对于一类复杂投影空间的Calabi-yau高度曲面的最大归化家族，我们研究了相关的非架构和热带蒙奇 - 安培方程，分别在相关的Berkovich空间以及其中的必不可少的骨架上进行。对于骨骼上的对称度量，我们证明热带方程式允许一个独特的解决方案，最多可添加常数。此外，对非架构方程的解决方案可以从热带解决方案中得出，并且是对射影空间上连续半阳性感谢您的限制。加上杨李的工作，这意味着在我们的环境中存在特殊拉格朗日纤维的弱公制猜想。
For a class of maximally degenerate families of Calabi-Yau hypersurfaces of complex projective space, we study associated non-Archimedean and tropical Monge-Ampère equations, taking place on the associated Berkovich space, and the essential skeleton therein, respectively. For a symmetric measure on the skeleton, we prove that the tropical equation admits a unique solution, up to an additive constant. Moreover, the solution to the non-Archimedean equation can be derived from the tropical solution, and is the restriction of a continuous semipositive toric metric on projective space. Together with the work of Yang Li, this implies the weak metric SYZ conjecture on the existence of special Lagrangian fibrations in our setting.
