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arXiv · 2608.28471

On Manin's conjecture for quartic del Pezzo fibrations

Sho Tanimoto
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Abstract

We generalize the homological sieve method, developed by Das, Lehmann, Tosteson, and the author, to study certain quartic del Pezzo fibrations, and we prove a version of Manin's conjecture over global function fields in these cases. Our proofs combine the $3$-dimensional positive-characteristic minimal model program, the geometry of the space of sections and the Abel--Jacobi mapping, and the homological sieve method. Our quartic del Pezzo surfaces have Picard rank $2$, and admit two birational morphisms to non-split quadric surfaces. In particular, they do not possess any conic fibrations.

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Sho Tanimoto. 2026-08-28. On Manin's conjecture for quartic del Pezzo fibrations. https://arxiv.org/abs/2608.28471

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