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Feb. 8, 2020. 19:30
|Preliminary meeting. Mainly organizational details, finalizing list of talks, etc.|
Feb. 15, 2020. 19:30
Fundamentals of Algebraic Geometry. Set up (Noetherian rings), algebraic sets, correspondences between ideals and algebraic sets, Hilbert's Basis Theorem and Hilbert's Nullstellensatz.
|Feb. 23. 2020.19:30||Kaleny, Bishoy|
Functions on varieties. section 4 (Reid)
|Feb 29. 2020. 19:30||Devkota, Prabhat||Hyperelliptic curves|
|Mar 07. 2020.|
Rudimentary Sheaf Cohomology. Exactness, complexes, and (co)homology. Sheaves, Sheaf Cohomolgoy, a finiteness theorem, Dolbeault's Theorem, deRham's theorem.
Mar 15. 2020.
Divisors and Line Bundles. Recalling the notion of a divisor in the context of sheaves. Defining line bundles, the Picard group and associated line bundles.
References: Chapter 1 (Griffith & Harris)
|Serre Duality and the Adjunction Formula. See See this file. The notes are meant to be read together with both roadmaps.|
Saturdays 19:15. Seminar Room, Research 1
- Reid "Undergraduate Algebraic Geometry" – Chapter 2 sections 3 and 4.
- Forster "Lectures on Riemann Surfaces" – Sections 6 and 12 – 15.
- Griffiths & Harris "Principles in Algebraic Geometry" - Chapter 1