F理论的数学基础/八维杂合弦对偶
Mathematics Underlying the F-Theory/Heterotic String Duality in Eight Dimensions
摘要：
弦论中的对偶之一，八维空间中的F理论/杂化弦对偶，预言了两个看似完全不同的几何对象之间有趣的对应。在对偶性的一侧有椭圆纤维K3曲面与部分。另一方面，人们发现椭圆曲线被赋予某些平坦的连接和复杂的Kahler类。本文是一个项目的一部分，旨在建立严格的数学结果描述几何基础的经典方面，这种对偶性。任务包括理解和比较两边的经典模空间。
英文摘要：
One of the dualities in string theory, the F-theory/heterotic string duality in eight dimensions, predicts an interesting correspondence between two seemingly disparate geometrical objects. On one side of the duality there are elliptically fibered K3 surfaces with section. On the other side, one finds elliptic curves endowed with certain flat connections and complexified Kahler classes. This paper is part of a project aimed at establishing the rigorous mathematical results describing the geometry underlying the classical aspects of this duality. The task involves understanding and comparing the classical moduli spaces on the two sides.
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