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Schedule

DateSpeakersDetails

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.

References: Section 3 (Reid)

Feb. 23. 2020.19:30Kaleny, Bishoy

Functions on varieties. section 4 (Reid)


Feb 29. 2020. 19:30Devkota, PrabhatHyperelliptic curves
Mar 07. 2020.
19:15

Rudimentary Sheaf Cohomology. Exactness, complexes, and (co)homology. Sheaves, Sheaf Cohomolgoy, a finiteness theorem, Dolbeault's Theorem, deRham's theorem.

References: See this file for references to all results that were discussed in the talk.

Mar 15. 2020.

19:00

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.


Meeting time

Saturdays 19:15. Seminar Room, Research 1


Participants

Pal, Abhik Devkota, Prabhat Irungu, Martin Waiharo Weiss, Nicolas Alexander Oprea, Maria Antonia Kaleny, Bishoy


References

  • 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