Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
Lectures on complex geometry, Calabi-Yau manifolds and toric geometry
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复几何、卡拉比-丘流形和复曲面几何讲座
DOI：
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发表时间：
2007
期刊：
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通讯作者：
V. Bouchard
中科院分区：
文献类型：
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作者：
V. Bouchard
这些是关于复几何、卡拉比-丘流形和环面几何的介绍性讲义。我们首先定义复几何和卡勒几何的基本概念。然后我们继续分析 Calabi-Yau 流形的各种定义。最后一节提供了对环面几何的简短介绍，旨在以两种不同的方式构造卡拉比-丘流形：作为环面簇中的超曲面和作为局部环面卡拉比-丘三重。这些讲稿是作者在 2005 年 Modave 数学物理暑期学校和 2007 年在 CERN 教授的迷你课程的补充。
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways: as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course that was given by the author at the Modave Summer School in Mathematical Physics 2005, and at CERN in 2007.