Algebraic geometry (Borcherds)

Richard Borcherds: Algebraic geometry, XVIII. Products of varieties

31st May, 2020

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The previous lecture in this series is here. The next lecture in this series is here.

This lecture covers products of affine and projective varieties and the Segre embedding.

This video is part of a lecture course by Richard Borcherds from 2020.

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

Richard Borcherds: Algebraic geometry, XVIII. Products of varieties

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