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Calabi-Yau Metrics with Cone Singularities along Intersecting Complex Lines: The Unstable Case
发布时间: 2021-07-09        浏览次数: 172

题目: Calabi-Yau Metrics with Cone Singularities along Intersecting Complex Lines: The Unstable Case
报告人: Matrin de Borbon  (Université de Nantes)
地点: zoom会议室
时间: 2020年7月9日 20: 00
摘要: In collaboration with G. Edwards we produce (local) Calabi-Yau metrics, in two complex dimensions, with cone singularities along intersecting complex lines, for cone angles that strictly violate the Troyanov condition. We identify the tangent cone at the origin as a product of two 2-cones. In the tangent cone limit, the line with the smallest cone angle remains apart while the other lines collide into a single cone factor. 
To prove our result, we first write an approximate solution with the desired asymptotic behavior and small Ricci potential. The main difficulty is to invert the Laplacian of such approximate solution metric in suitable Holder spaces. Once this is done, we use the implicit function theorem to perturb into an actual Calabi-Yau metric.
时间: 2020年7月9日 20: 00 
参会方式: Zoom 会议室 
注册链接: http://zoom.us/meeting/register/tJMvfu6qpjsiGNLBhF24-mHtH8uPPHjX6Dxu

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