Algebraic Curves
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This course is a follow-up to last semester's course on Commutative Algebra. See the typed lecture notes.
This semester we will cover "one dimensional mathematics." This is based on the amazing 19th century synthesis of three seemingly different subjects: - Algebraic Curves: Sets in the plane defined by a single polynomial equation f(x,y)=0. - Riemann Surfaces: One dimensional compact complex manifolds. - Function Fields: Field extensions over the complex numbers of transcendence degree one. Lecture: 2:30--3:45 TuTh on Zoom Office Hours: After the lecture | ||
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Introduction |
Jan 25 Notes Jan 26 Notes Jan 28 Notes |
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Zariski Topology Homework 1 |
Feb 2 Notes Feb 4 Notes |
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Projective Geometry |
Feb 9 Notes Feb 11 Notes Feb 16 Notes [Maple Worksheet] |
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Singular Points |
Feb 18 Notes Feb 23 Notes Feb 25 Notes |
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Bezout's Theorem |
Mar 2 Notes Mar 4 Notes |
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Applications of Bezout Homework 2 |
Mar 9 Notes Mar 11 Notes |
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Cubic Curves |
Mar 16 Notes [Maple Worksheet] Mar 18 Notes |
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Idea of a Riemann Surface |
Mar 23 Notes Mar 25 Notes Mar 30 Notes |
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Meromorphic Functions, Riemann-Hurwitz |
Apr 1 Notes Apr 6 Notes |
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Harnack's Theorem, Segre Embedding |
Apr 8 Notes Apr 13 Notes Apr 15 Notes |
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Secant Variety, Function Field, Ran Out of Time |
Apr 20 Notes Apr 22 Notes Apr 27 Notes |
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