Abstract

In this chapter, we explain the basics of geometry of complex manifolds, which will help the readers to understand the results of mirror symmetry. First, we introduce the definition of complex manifolds and holomorphic vector bundles on complex manifolds. We also discuss Chern classes of holomorphic vector bundles. Then we introduce K\(\ddot{\text {a}}\)hler manifolds, which play a central role in geometry of complex manifolds, and explain various characteristics of projective space, which is the most important example in this book. Lastly, we discuss the outline of the notion of an orbifold, which appears in various aspects of mirror symmetry. (For deeper understanding of complex geometry, we recommend readers to consult [1].)

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