250145 VO Algebraic Geometry III (2023S)
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Registration/Deregistration
Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes
This course with two weekly hours will be held in blocked form, thus having in the respective weeks 3 hours per week. The foreseen periods are:
Monday March 6 - Friday March 24: three weeksMonday April 24 - Friday June 9: seven weeksInformation
Aims, contents and method of the course
The course will introduce fundamental techniques and results in the theory of schemes. Even though being a continuation of Alg Geom II, newcomers are welcome (and can get the notes of the former course).Prospective topics are as follows (there will be some flexibility in our choice):Graded rings and projective schemes, with the example of elliptic curves and blowups.Gluing of affine schemes to construct general schemes.Properties of morphisms: Semicontinuity of fiber dimension, Chevalley's theorem about the image of constructible sets, flat morphisms, isomorphisms and automorphism groups. Group schemes and moduli spaces.Singularities: Normalization and integral closure, blowups, resolution of singularities.Dimension theory: Hilbert functions and Hilbert polynomials.
Assessment and permitted materials
Oral exams upon appointment.
Minimum requirements and assessment criteria
Examination topics
Reading list
Mumford: Red book on Varieties
Hartshorne: Algebraic Geometry
Shafarevich: Introduction to Algebraic Geometry.
Hartshorne: Algebraic Geometry
Shafarevich: Introduction to Algebraic Geometry.
Association in the course directory
MALV, MGEV
Last modified: Tu 26.09.2023 10:08