Complex and Kähler Geometry
Complex manifolds, Kähler metrics, and Calabi–Yau structures.
Complex and Kähler Geometry. Complex manifolds, Kähler metrics, and Calabi–Yau structures.
Foundations and canonical references
The standard treatments of complex and kähler geometry approach the subject from complementary angles. Griffiths, Principles of Algebraic Geometry (1978) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Huybrechts, Complex Geometry: An Introduction (2005) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for complex and kähler geometry include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1978Principles of Algebraic Geometrygriffiths-1978, harris-1978
- textbook · primary · 2005Complex Geometry: An Introductionhuybrechts-2005
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