The previous lecture in this series is here. The next lecture in this series is here.
This lecture gives an informal survey of complex curves of small genus.
This video is part of a lecture course by Richard Borcherds from 2020.
Algebraic geometry (Borcherds)
Richard Borcherds: Algebraic geometry, XLIV. Survey of curves
17th June, 2020
In This Lecture Course
- Richard Borcherds: Algebraic geometry, I. Introduction
- Richard Borcherds: Algebraic geometry, II. Two cubic curves
- Richard Borcherds: Algebraic geometry, III. Bezout, Pappus, Pascal
- Richard Borcherds: Algebraic geometry, IV. Kakeya sets
- Richard Borcherds: Algebraic geometry, V. Affine space and the Zariski topology
- Richard Borcherds: Algebraic geometry, VI. Noetherian spaces
- Richard Borcherds: Algebraic geometry, VII. Weak Nullstellensatz
- Richard Borcherds: Algebraic geometry, VIII. Strong Nullstellensatz
- Richard Borcherds: Algebraic geometry, IX. The Lasker-Noether theorem
- Richard Borcherds: Algebraic geometry, X. The proof of the Lasker-Noether theorem
- Richard Borcherds: Algebraic geometry, XI. Quotients of varieties by groups
- Richard Borcherds: Algebraic geometry, XII. Hilbert’s finiteness theorem
- Richard Borcherds: Algebraic geometry, XIII. Three examples of quotients
- Richard Borcherds: Algebraic geometry, XIV. Dimension
- Richard Borcherds: Algebraic geometry, XV. Projective space
- Richard Borcherds: Algebraic geometry, XVI. Desargues’s theorem
- Richard Borcherds: Algebraic geometry, XVII. Affine and projective varieties
- Richard Borcherds: Algebraic geometry, XVIII. Products of varieties
- Richard Borcherds: Algebraic geometry, XIX. The Veronese surface and the variety of lines in space
- Richard Borcherds: Algebraic geometry, XX. Grassmannians
- Richard Borcherds: Algebraic geometry, XXI. Projective space bundles
- Richard Borcherds: Algebraic geometry, XXII. Toric varieties
- Richard Borcherds: Algebraic geometry, XXIII. Categories
- Richard Borcherds: Algebraic geometry, XXIV. Regular functions
- Richard Borcherds: Algebraic geometry, XXV. Morphisms of varieties
- Richard Borcherds: Algebraic geometry, XXVI. Affine algebraic sets and commutative rings
- Richard Borcherds: Algebraic geometry, XXVII. The twisted cubic
- Richard Borcherds: Algebraic geometry, XXVIII. Products of projective varieties
- Richard Borcherds: Algebraic geometry, XXIX. Automorphisms of space
- Richard Borcherds: Algebraic geometry, XXX. The Ax-Grothendieck theorem
- Richard Borcherds: Algebraic geometry, XXXI. Rational maps
- Richard Borcherds: Algebraic geometry, XXXII. Elliptic functions and cubic curves
- Richard Borcherds: Algebraic geometry, XXXIII. Rationality of cubic surfaces
- Richard Borcherds: Algebraic geometry, XXXIV. Blowing up a point
- Richard Borcherds: Algebraic geometry, XXXV. More on blowups
- Richard Borcherds: Algebraic geometry, XXXVI. The Atiyah flop
- Richard Borcherds: Algebraic geometry, XXXVII. Singular points
- Richard Borcherds: Algebraic geometry, XXXVIII. The Zariski tangent space
- Richard Borcherds: Algebraic geometry, XXXIX. Du Val singularities
- Richard Borcherds: Algebraic geometry, XL. Examples of resolutions
- Richard Borcherds: Algebraic geometry, XLI. Completions
- Richard Borcherds: Algebraic geometry, XLII. Resultants
- Richard Borcherds: Algebraic geometry, XLIII. Proper maps
- Richard Borcherds: Algebraic geometry, XLIV. Survey of curves
- Richard Borcherds: Algebraic geometry, XLV. Hurwitrz curves
- Richard Borcherds: Algebraic geometry, XLVI. Examples of Hurwitz curves
- Richard Borcherds: Algebraic geometry, XLVII. Resolution of curve singularities
- Richard Borcherds: Algebraic geometry, XLVIII. Newton’s rotating ruler
- Richard Borcherds: Algebraic geometry, XLIX. Hilbert polynomials
- Richard Borcherds: Algebraic geometry, L. The degree of a projective variety
- Richard Borcherds: Algebraic geometry, LI. Bazout’s theorem