An overview of Manin's conjecture for del Pezzo surfaces

Abstract

This paper surveys recent progress towards the Manin conjecture for (singular and non-singular) del Pezzo surfaces. To illustrate some of the techniques available, an upper bound of the expected order of magnitude is established for a singular del Pezzo surface of degree four.

18 pages

References in corpus (2)

• The density of rational points on Cayley's cubic surface
• Manin's conjecture for a certain singular cubic surface

Cited by in corpus (8)

• Campana points on biequivariant compactifications of the Heisenberg group
• Asymptotic behaviour of rational curves
• Manin's conjecture on a nonsingular quartic del Pezzo surface
• The Manin conjecture in dimension 2
• On Manin's conjecture for singular del Pezzo surfaces of degree four, II
• Universal torsors of Del Pezzo surfaces and homogeneous spaces
• On a constant arising in Manin's conjecture for Del Pezzo surfaces
• Movable Bend and Break for sections of del Pezzo fibrations