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Classifying sections of
del Pezzo fibrations, II
Brian Lehmann and Sho Tanimoto |
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Geometry & Topology 26 (2022) 2565–2647
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DOI: 10.2140/gt.2022.26.2565
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Abstract |
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Let be a del Pezzo surface over the function field of a complex curve. We study the behavior of rational points on leading to bounds on the counting function in the geometric Manin 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 the geometric Manin conjecture for certain split del Pezzo surfaces of degree admitting a birational morphism to over the ground field. |
Keywords
section, del Pezzo fibration, Fujita invariant, geometric
Manin's conjecture
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Mathematical Subject Classification
Primary: 14H10
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References |
Publication
Received: 15 July 2020
Revised: 10 June 2021
Accepted: 8 July 2021
Published: 13 December 2022
Proposed: Dan Abramovich
Seconded: Mark Gross, Benson Farb
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Authors |
| Brian Lehmann | |
| Department of Mathematics Boston College Chestnut Hill, MA United States |
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| Sho Tanimoto | |
| Graduate School of Mathematics Nagoya University Nagoya Japan |
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