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65-413 Algebraic Geometry
| Lecturer: |
Bernd Siebert
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| Recitations: |
Lisa Bauer
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| Content: |
This class gives a first introduction into algebraic geometry with an emphasis on the relation between geometry and algebra. The central concept is that of a variety over a field, given by a number of polynomial equations.
The geometric view on algebra has a long and rich history. Today algebraic geometry with its various ramifications provides one of the central techniques in pure mathematics.
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| Aim: |
Basic concepts of commutative algebra: ideals, quotient rings, localization, Krull dimension, Hilbert's Nullstellensatz, basic dimension theory, completion.
Affine varieties, projective varieties, standard constructions of projective algebraic geometry, blowing up, regular and rational morphisms, smooth versus singular points, the category of algebraic curves over a field and function fields of transcendence degree one, basic intersection theory.
Sheaves and cohomology
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| Approach |
We mostly follow Chapter 1 in Hartshorne's "Algebraic geometry", including most of the exercises. Recitations will be an integral part of the classes.
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| Literature: |
Atiyah, Macdonald: Introduction to Commutative Algebra, Addison-Wesley 1969
Hartshorne: Algebraic Geometry, Springer 1977
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| Module: |
Ma-M-VAlgGeom_n |
| Lecture: |
Tuesday, 10:00-11:30, H3
Friday, 12:00-13:30, H4
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| Recitations: |
Tuesday, 08:15-09:45, Rm 241
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| Exam: |
oral exam |
| Exercise sheets: |
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