The spaces of rational curves on del Pezzo surfaces via conic bundles

[2506.18239] The spaces of rational curves on del Pezzo surfaces via conic bundles Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2506.18239 (math) [Submitted on 23 Jun 2025 ( v1 ), last revised 11 Apr 2026 (this version, v3)] Title: The spaces of rational curves on del Pezzo surfaces via conic bundles Authors: Sho Tanimoto View a PDF of the paper titled The spaces of rational curves on del Pezzo surfaces via conic bundles, by Sho Tanimoto View PDF HTML (experimental) Abstract: Using the homological sieve method developed by Das--Lehmann--Tosteson and the author, we prove Peyre's all height approach to Manin's conjecture for split quintic del Pezzo surfaces defined over $\mathbb F_q(t)$ assuming $q$ is sufficiently large. We also establish lower bounds of correct magnitude for the counting function of rational curves on split low degree del Pezzo surfaces defined over $\mathbb F_q$ assuming $q$ is large. Comments: minor revision, 36 pages, to appear in Simons Symposia "Geometry over non-closed fields" Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT) Cite as: arXiv:2506.18239 [math.AG] (or arXiv:2506.18239v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2506.18239 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sho Tanimoto [ view email ] [v1] Mon, 23 Jun 2025 02:11:11 UTC (24 KB) [v2] Sat, 24 Jan 2026 11:26:07 UTC (26 KB) [v3] Sat, 11 Apr 2026 15:23:50 UTC (26 KB) Full-text links: Access Paper: View a PDF of the paper titled The spaces of rational curves on del Pezzo surfaces via conic bundles, by Sho Tanimoto View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2025-06 Change to browse by: math math.NT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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