The Rigid Limit in Special Kahler Geometry: From K3-Fibrations to Special Riemann Surfaces: A Detailed Case Study
The Rigid Limit in Special Kahler Geometry: From K3-Fibrations to Special Riemann Surfaces: A Detailed Case Study
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特殊卡勒几何中的刚性极限：从 K3 纤维到特殊黎曼曲面：详细案例研究
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发表时间：
1998
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通讯作者：
D. Zanon
中科院分区：
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作者：
M. Billó;F. Denef;P. Fré;I. Pesando;W. Troost;A. Proeyen;D. Zanon
研究了特殊Kahler流形在某些奇点邻域内的模空间到其刚性极限的极限过程。在两个例子中，我们考虑所有的周期和周围的刚性极限，确定非平凡的极限作为相关的黎曼曲面上的亚纯形式的周期。我们展示了特殊的Kahler流形的Kahler势如何约化为刚性的特殊Kahler流形的Kahler势。我们广泛使用这些Calabi-Yau流形的结构作为K3纤维化，这对于获得K3退化到极限ALE流形之前的周期是有用的。我们研究了计算周期的各种方法及其性质。这些方法的发展是获得Calabi-Yau流形上超引力精确结果的重要一步。
The limiting procedure of special Kahler manifolds to their rigid limit is studied for moduli spaces of Calabi-Yau manifolds in the neighbourhood of certain singularities. In two examples we consider all the periods in and around the rigid limit, identifying the non-trivial ones in the limit as periods of a meromorphic form on the relevant Riemann surfaces. We show how the Kahler potential of the special Kahler manifold reduces to that of a rigid special Kahler manifold. We make extensive use of the structure of these Calabi-Yau manifolds as K3 fibrations, which is useful to obtain the periods even before the K3 degenerates to an ALE manifold in the limit. We study various methods to calculate the periods and their properties. The development of these methods is an important step to obtaining exact results from supergravity on Calabi-Yau manifolds.