Classifying sections of del Pezzo fibrations, II

Abstract

Let $X$ be a del Pezzo surface over the function field of a complex curve. We study the behavior of rational points on $X$ leading to bounds on the counting function in Geometric Manin's Conjecture. A key tool is the Movable Bend and Break Lemma which yields an inductive approach to classifying relatively free sections for a del Pezzo fibration over a curve. Using this lemma we prove Geometric Manin's Conjecture for certain split del Pezzo surfaces of degree $\ge 2$ admitting a birational morphism to ${\mathbb{P}}^2$ over the ground field.

60 pages, to appear in Geometry & Topology

References in corpus (1)

• Asymptotic behaviour of rational curves

Cited by in corpus (2)

• An introduction to Geometric Manin's conjecture
• Movable Bend and Break for sections of del Pezzo fibrations