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Teaching: Course "Algebraic Curves"
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Overview
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| Course: | Math 255 - Section 1 - Algebraic Curves |
| Term: | Spring 2009 |
| Link to bookmark: | math.berkeley.edu/~waldorf/algebraiccurves |
| Control Number: | 54746 |
| Lectures: | Tuesdays 3:30pm-5:00pm, Room 81 Evans
Thursdays 11:00am-12:30pm, Room 891 Evans |
Contact
Contents
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1. Riemann surfaces, 2. Functions and maps, 3. Examples of Riemann surfaces, 4. Integration on Riemann surfaces, 5. Divisors and meromorphic Functions, 6. Algebraic Curves, 7. Applications of Riemann-Roch, 8. Sheaves and Cech Cohomology, 9. Line Bundles.
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Exercises
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Exercise I (
 pdf): "Meromorphic Functions on Complex Tori"
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Exercise II (pdf): "Classification of Complex Tori"
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Exercise III (pdf): "Examples of Divisors on Algebraic Curves"
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Exercise IV (pdf): "Castelnuovo's Bound"
Prerequisites
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Point-set topology (202A),
groups, rings and fields (the basics of 250A, or 114), complex analysis (185).
Literature
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The course essentially follows [1]. The book [2] is similar, but a bit more elementary.
[3] is the reference for elliptic curves, and [4] is a standard book on more advanced algebraic geometry.
If you are interested in the topological aspects, you might want to have a look in [5,6].
| [1] | |
R. Miranda, Algebraic Curves and Riemann Surfaces, Graduate Studies in Mathematics, AMS, 1995. |
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| [2] | |
F. Kirwan, Complex Algebraic Curves, Cambridge University Press, 1992. |
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| [3] | |
J. S. Milne, Elliptic Curves, Kea Books, 2006. |
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| [4] | |
R. Hartshorne, Algebraic Geometry, Gratuate Text in Mathematics, Springer, 1977. |
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| [5] | |
W. Fulton, Algebraic Topology, A First Course, Gratuate Text in Mathematics, Springer, 1997. |
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| [6] | |
F. Hirzebruch, Topological Methods in Algebraic Geometry, Grundlehren der Mathematischen Wissenschaften, Springer, 1978. |
Note: none of these books is required.
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