ementas

Introduction to Complex Geometry MAT2256

Syllabus

• Holomorphic functions in several variables.
• Complex varieties.
• Kähler metrics.
• Blow-up.
• Complex vector bundles, connections, curvature, Chern classes.
• Sheaves and cohomology.
• Harmonic forms, Hodge theorem and applications. (cf. Hodge theory)
• Kähler identities, Hodge decomposition.
• Serre-Kodaira duality.
• Lefschetz decomposition.
• Divisors and line bundles.
• Bertini theorem.
• Adjunction formula.
• Kodaira’s vanishing theorem.
• Lefschetz’s theorem on hyperplane sections.
• Lefschetz’s theorem on (1,1) classes.
• Algebraic varieties.
• Chow’s theorem.
• Kodaira’s immersion theorem.
• Picard and Albanese varieties.
• Applications.

Basic Bibliography:

1. Phillip Griffiths and Joe Harris: Principles of Algebraic Geometry, Wiley-Interscience, 1994.
2. Claire Voisin: Théorie de Hodge et Géometrie Algébrique Complexe, Societe Mathematique de France, 2002.
3. Daniel Huybrechts: Complex Geometry, Springer-Verlag, 2004.