Rational varieties: algebra, geometry and arithmetic

CONTENTS Introduction § 1. Curves: geometry and arithmetic § 2. Surfaces: geometry over a closed field § 3. Surfaces: geometry over a non-closed field § 4. k -birational invariants § 5. Torsors and descent § 6. Zero-cycles and K -theory § 7. Surfaces: a little more geometry, combinatorics and arithmetic § 8. Varieties of dimension ≥3: geometry § 9. Higher dimensional intersections of a pair of quadrics: arithmetic § 10. Open problems References