The previous lecture in this series is here. The next lecture in this series is here.
This lecture describes an example of a birational map called the Atiyah flop.
This video is part of a lecture course by Richard Borcherds from 2020.
Algebraic geometry (Borcherds)
Richard Borcherds: Algebraic geometry, XXXVI. The Atiyah flop
13th 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