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Created by:
Last updated:
November 7, 2022
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
Description
The main aims of this seminar will be to go over
the classification of surfaces (Enriques-Castelnuovo for characteristic zero, Bombieri-Mumford for characteristic p), while working out plenty of examples, and treating their geometry and arithmetic as far as possible.
Course Curriculum
- Introduction Unlimited
- Linear equivalence, algebraic equivalence, numerical equivalence of divisors Unlimited
- Birational maps, rational maps, linear systems, properties of birational maps between surfaces Unlimited
- Birational maps (cont.) Unlimited
- Ruled surfaces I Unlimited
- Ruled surfaces II Unlimited
- Ruled surfaces III, rational surfaces Unlimited
- Linear systems, rational normal scrolls Unlimited
- Castelnuovo’s criterion for rationality Unlimited
- Picard variety Unlimited
- Albanese variety Unlimited
- Non-ruled and ruled surfaces Unlimited
- Classification of ruled surfaces Unlimited
- Elliptic and quasi-elliptic surfaces Unlimited
- Elliptic surfaces (cont.), Kodaira dimension 0 Unlimited
- K3 surfaces Unlimited
- Enriques surfaces, bielliptic surfaces Unlimited
- Classification Unlimited
- Elliptic/quasi-elliptic fibrations I Unlimited
- Elliptic/quasi-elliptic fibrations II Unlimited
- Elliptic/quasi-elliptic fibrations III, classification Unlimited
- Moduli Unlimited
About the instructor
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5
Instructor Rating
1
Reviews
1520
Courses
1916
Students
Massachusetts Institute of Technology
