Maths - Algebraic Geometry

Algebraic geometry is about applying geometrical constructions to algebraic problems.

Or, to turn this around, its about geometric structures defined by polynomials.
  • Set theory has functions.
  • Topology has continuous functions.
  • Differential geometry has smooth functions.
  • Analytic geometry has analytic functions.
  • Algebraic geometry has polynomial functions.
Main objects in algebraic geometry are algebraic varieties.

Videos

Fields Medal Lecture: Classification of algebraic varieties — Caucher Birkar — ICM2018 Youtube.

Algebraic geometry - Richard E. BORCHERDS

  1. Introduction - https://www.youtube.com/watch?v=JZKDmTIFR7A
  2. Two cubic curves - https://www.youtube.com/watch?v=SxGqKIALcgI
  3. Bezout, Pappus, Pascal - https://www.youtube.com/watch?v=-9qugwEZDJs
  4. Kakeya sets - https://www.youtube.com/watch?v=0I4ThQGwr3Y
  5. Affine space and the Zariski topology - https://www.youtube.com/watch?v=GQTwEMhbQ4k
  6. Noetherian spaces - https://www.youtube.com/watch?v=D_eJ8BWLb24
  7. weak nullstellensatz - https://www.youtube.com/watch?v=hBQXqIkUUyY

Computational Algebraic Geometry

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Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

cover 3D Math Primer - Aimed at complete beginners to vector and matrix algebra.

Other Math Books

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