Rational curves on del Pezzo surfaces in positive characteristic
Rational curves on del Pezzo surfaces in positive characteristic
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DOI：
10.1090/btran/138
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发表时间：
2021-10
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影响因子：
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通讯作者：
Roya Beheshti;Brian Lehmann;Eric Riedl;Sho Tanimoto
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文献类型：
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作者：
Roya Beheshti;Brian Lehmann;Eric Riedl;Sho Tanimoto
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，我们证明了给定nef类的有理曲线的模空间的不可约性，推广了Testa在特征0 0中的结果.我们还研究了弱del Pezzo曲面的几何Manin猜想的原理。在研究过程中，我们给出了定义在F2(T)\mathbb F2(T)或F3(T)\mathbb{F}{3}(T)上的弱del Pezzo曲面的例子，使得Manin猜想中的例外集是Zariski稠密的.
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.