MA4A5
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Course DescriptionAlgebraic geometry studies the geometry of spaces defined by polynomial equations. This module will study affine and projective varieties, focusing on examples and the dictionary between algebra and geometry. See also the description in the PYDC booklet. | |||||||||||||
Lecturer
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Course Times and Location
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Recommended TextsWe will fairly closely follow Introduction to Algebraic Geometry by Brendan Hassett. Also highly recommended is Ideals, Varieties, and algorithms, by David Cox, John Little, and Donal O'Shea.Other references you may want to consult include Undergraduate Algebraic Geometry by Miles Reid, Algebraic Geometry by Joe Harris, and the lecture notes of Andreas Gathmann (this contains many topics we will not get to). Other more advanced references include the classic by Hartshorne, and Shafarevich. If you want to buy copies of any of these books, I recommend first looking at a site like Alibris.co.uk, which searches multiple independent bookstores. | |||||||||||||
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AssessmentThere will be homework assignments every two weeks. Homework assignments and due dates will be posted on the schedule webpage, which will also have the reading for the following week. You are encouraged to work on homework together, but you should write up the solutions yourself. No late homework will be accepted. The lowest homework score will be dropped, however, when calculating your homework mark. Homework will be due at 12pm on the Fridays indicated on the schedule page.In addition there will be a miniproject which will be due at the start of Term 2 (at 12pm on Tuesday, 10th January). Your final mark for this module will depend 20% on your homework, 10% on the mini-project, and 70% on the examination in Term 3. | |||||||||||||
Mini-projectThere are many possible first courses in algebraic geometry, and we cannot cover everything that might belong in such a course. In the mini-project you will learn one of these topics, and write a five page description of the topic at a level suitable for reading by your classmates. The five page page-limit will be strictly enforced, and the font must be at least 11pt. Deadlines:
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