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| 65-413/414: |
Module: Complex geometry
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| Lecturer: |
Bernd Siebert
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| Description: |
Complex geometry is the study of spaces endowed with holomorphic functions. The field connects the theory of complex functions in one variable ("Funktionentheorie") with differential geometry (differentiable functions) and algebraic geometry (polynomial functions). Complex geometry provides an ample source of examples for differential geometry, while providing the geometric picture for algebraic geometry.
While previous exposure to complex functions in one variable and differential geometry can occasionally be useful, the class will nevertheless not assume much more than the basic classes in analysis and linear algebra.
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| Content: |
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Local theory: holomorphic functions, differential forms, analytic sets.
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Complex manifolds: Topology, examples, divisors, line bundles, coverings, blow-ups.
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Kähler manifolds: Kähler identities, Hodge theory, Lefschetz theorems.
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| Prerequisites: |
Linear algebra I/II, Analysis I–III.
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| Literature: |
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D. Huybrechts: Complex Geometry, Springer Universitext 2005.
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P. Griffiths, J. Harris:Principles of Algebraic Geometry, Wiley 1978.
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| Time and venue: |
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Lecture: MON 16:15–17:45 Geom H3, THU 10:15–11:00 Geom H3
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Recitations: THU 11:00-11:45 Geom H3
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First class: 17.10.2016
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| Exam: |
Oral examination.
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| Exercises (PDF): |
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