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Algebraic Geometry

Lecturer: 
Course Type: 
PhD Course
Anno (LM): 
Second Year
Academic Year: 
2020-2021
Period: 
October-January
Duration: 
60 h
Description: 

The first 48 hours of the course form an introduction to the language of schemes and coherent sheaves, and cover the material in Hartshorne, Algebraic Geometry, Section II.1-II.8: sheaves; schemes; open and closed subschemes, affine, finite, projective morphisms; properness and separatedness; quasicoherent and coherent sheaves, pushforward and pullback; divisors and invertible sheaves; Proj construction and blow-ups, sheaf of differentials. The remaining 12 hours will cover a quick introduction to infinitesimal deformation theory: Artinian local algebras, deformation functors, Schlessinger axioms, tangent and obstruction spaces. Prerequisites are the basics of point set topology and a solid background in basic commutative algebra.In particular, we will need rings, subrings, quotient rings, prime and maximal ideals, noetherianity, localization; modules over a ring, kernels and cokernels, localization, tensor product. Previous knowledge of complex manifolds of quasiprojective varieties, while not logically necessary, would be useful to support intuition.

Location: 
A-005
Next Lectures: 
Thursday, October 29, 2020 - 14:00 to 16:00
Friday, October 30, 2020 - 16:00 to 18:00
Thursday, November 5, 2020 - 14:00 to 16:00
Friday, November 6, 2020 - 16:00 to 18:00
Thursday, November 12, 2020 - 14:00 to 16:00
Friday, November 13, 2020 - 16:00 to 18:00
Thursday, November 19, 2020 - 14:00 to 16:00
Friday, November 20, 2020 - 16:00 to 18:00
Thursday, November 26, 2020 - 14:00 to 16:00
Friday, November 27, 2020 - 16:00 to 18:00
Thursday, December 3, 2020 - 14:00 to 16:00
Friday, December 4, 2020 - 16:00 to 18:00
Thursday, December 10, 2020 - 14:00 to 16:00
Friday, December 11, 2020 - 16:00 to 18:00
Thursday, December 17, 2020 - 14:00 to 16:00
Friday, December 18, 2020 - 16:00 to 18:00
Thursday, January 7, 2021 - 14:00 to 16:00
Friday, January 8, 2021 - 16:00 to 18:00
Thursday, January 14, 2021 - 14:00 to 16:00
Friday, January 15, 2021 - 16:00 to 18:00
Thursday, January 21, 2021 - 14:00 to 16:00
Friday, January 22, 2021 - 16:00 to 18:00
Thursday, January 28, 2021 - 14:00 to 16:00
Friday, January 29, 2021 - 16:00 to 18:00

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