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arXiv · 2506.18239

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

Sho Tanimoto
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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.

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Sho Tanimoto. 2025-06-23. The spaces of rational curves on del Pezzo surfaces via conic bundles. https://arxiv.org/abs/2506.18239

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