杂种优势层、Monge-Ampere方程和del Pezzo曲面
Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces
摘要：
保4超对称的杂化视界有截面是6维共形平衡厄米流形上的T^2纤维化。我们给出了截面为S^3 × S^3 × T^2和SU（3）的视界的新例子。然后我们研究了Kahler四维流形上的T^4纤维化的杂化视界。我们证明了解决方案取决于6个功能，这是由一个非线性微分系统的6个方程，其中包括蒙赫-安培方程。我们证明了这个系统对于Kahler流形S^2 × S^2有一个显式解。我们还证明了存在一个相关的上同调系统，它有delPezzo曲面上的解决方案。我们提出的问题是，对于上同调问题的每一个解，是否都有一个微分系统的解，从而有一个新的杂种视界。视界截面的拓扑结构包括（（k-1）S^2 × S^4 # k（S^3 × S^3））× T^2$，表明奇异黑洞的存在。我们还发现了一个例子的地平线部分，这引起了两个不同的近地平线几何。
英文摘要：
Heterotic horizons preserving 4 supersymmetries have sections which are T^2 fibrations over 6-dimensional conformally balanced Hermitian manifolds. We give new examples of horizons with sections S^3 X S^3 X T^2 and SU(3). We then examine the heterotic horizons which are T^4 fibrations over a Kahler 4-dimensional manifold. We prove that the solutions depend on 6 functions which are determined by a non-linear differential system of 6 equations that include the Monge-Ampere equation. We show that this system has an explicit solution for the Kahler manifold S^2 X S^2. We also demonstrate that there is an associated cohomological system which has solutions on del Pezzo surfaces. We raise the question of whether for every solution of the cohomological problem there is a solution of the differential system, and so a new heterotic horizon. The horizon sections have topologies which include ((k-1) S^2 X S^4 # k (S^3 X S^3)) X T^2$ indicating the existence of exotic black holes. We also find an example of a horizon section which gives rise to two different near horizon geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
