Lifting negative curves from finite fields and Seshadri constants at ten points

Piotr Pokora; Tomasz Szemberg

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arXiv · 2610.06225

Lifting negative curves from finite fields and Seshadri constants at ten points

Piotr Pokora·Tomasz Szemberg

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Abstract

We use finite-field calculations and mixed-characteristic deformation to construct nef divisors on very general complex blow-ups of the plane. A lifting and smoothing criterion converts a reducible nodal divisor over $\mathbb{F}_{127}$ into a smooth genus-$10$ curve of class $117H-37(E_1+\cdots+E_{10})$, retaining control of its first-order obstruction map. Its normal bundle in a suitable deformation is semistable, so Petrakiev's multiplicity estimate yields the nef class $27379H-8658(E_1+\cdots+E_{10})$ at ten very general points. Their multipoint Seshadri constant is therefore at least $8658/27379$, improving Petrakiev's bound $228/721$. The geometric input is an existence criterion in characteristic zero verified by computations in positive characteristic.

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BibTeX RIS

Piotr Pokora, Tomasz Szemberg. 2026-10-05. Lifting negative curves from finite fields and Seshadri constants at ten points. https://arxiv.org/abs/2610.06225

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