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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 this file. The notes are meant to be read together with both roadmaps.|
|Mar 29, 2020. 19:15||Discussion: COVID-19 + new seminar format.|
|Apr 4, 2020. 19:15|
|Apr. 26, 2020. 19:15||Oprea, Maria Antonia||Poincaré Duality.|
|May 2, 2020. 19:15||Cremona Group and its finite order subgroups. |
References: Igor V. Dolgachev, Vasily A. Iskovskikh "Finite subgroups of the plane Cremona group" and Jérémy Blanc "Elements and cyclic subgroups of finite order of the Creoma group".
|May 3, 2020, 19:30||Weiss, Nicolas Alexander|
Describing canonical bundles as associated bundles, defining Iitake and Kodaira dimension and putting the adjunction formula into perspective for classification of surfaces in P_3. Introducing K3 surfaces and Quartics and Kummer surfaces as prominent examples.
|May 10, 2020, 19:30||Devkota, Prabhat|
Mori Theory and Classification of surfaces.
Seminar Room, Research 1 (pre COVID-19)
Teams (post COVID-19)
- 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 and 4
- Yuri Manin, "Cubic Forms" - Chapter IV
- Igor V. Dolgachev, Vasily A. Iskovskikh "Finite subgroups of the plane Cremona group"
- Jérémy Blanc "Elements and cyclic subgroups of finite order of the Creoma group".