del Pezzo曲面上具有正特征的有理曲线

Transactions of the American Mathematical Society, Series B Pub Date : 2021-10-01 DOI:10.1090/btran/138

Roya Beheshti, Brian Lehmann, Eric Riedl, Sho Tanimoto

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引用次数: 7

摘要

研究了del Pezzo曲面上具有正特征的有理曲线空间。对于大多数素数p p，证明了给定nef类的有理曲线模空间的不可约性，推广了Testa在特征0 0上的结果。我们还研究了弱del Pezzo曲面的几何Manin猜想的原理。在本研究过程中，我们给出了在f2 (t) \mathbb F_2(t)或f3 (t) \mathbb {F}_{3}(t)上定义的弱del Pezzo曲面的例子，使得Manin猜想中的例外集是Zariski密集的。

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Rational curves on del Pezzo surfaces in positive characteristic

We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 0 0 . We also investigate the principles of Geometric Manin’s Conjecture for weak del Pezzo surfaces. In the course of this investigation, we give examples of weak del Pezzo surfaces defined over F 2 ( t ) \mathbb F_2(t) or F 3 ( t ) \mathbb {F}_{3}(t) such that the exceptional sets in Manin’s Conjecture are Zariski dense.

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Transactions of the American Mathematical Society, Series B

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1.70

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