Rational curves on del pezzo surfaces in positive characteristic

Roya Beheshti; Brian Lehmann; Eric Riedl; Sho Tanimoto

doi:10.1090/btran/138

Rational curves on del pezzo surfaces in positive characteristic

Roya Beheshti
, Brian Lehmann
, Eric Riedl
, Sho Tanimoto

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 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 F₂(t) or F₃(t) such that the exceptional sets in Manin’s Conjecture are Zariski dense.

Original language	English
Pages (from-to)	407-451
Number of pages	45
Journal	Transactions of the American Mathematical Society Series B
Volume	10
DOIs	https://doi.org/10.1090/btran/138
State	Published - 2023

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abstract = "We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 0. We also investigate the principles of Geometric Manin{\textquoteright}s Conjecture for weak del Pezzo surfaces. In the course of this investigation, we give examples of weak del Pezzo surfaces defined over F2(t) or F3(t) such that the exceptional sets in Manin{\textquoteright}s Conjecture are Zariski dense.",

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AU - Beheshti, Roya

AU - Lehmann, Brian

AU - Riedl, Eric

AU - Tanimoto, Sho

PY - 2023

Y1 - 2023

N2 - We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 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 F2(t) or F3(t) such that the exceptional sets in Manin’s Conjecture are Zariski dense.

AB - We study the space of rational curves on del Pezzo surfaces in positive characteristic. For most primes p we prove the irreducibility of the moduli space of rational curves of a given nef class, extending results of Testa in characteristic 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 F2(t) or F3(t) such that the exceptional sets in Manin’s Conjecture are Zariski dense.

UR - https://www.scopus.com/pages/publications/85152466752

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DO - 10.1090/btran/138

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AN - SCOPUS:85152466752

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VL - 10

SP - 407

EP - 451

JO - Transactions of the American Mathematical Society Series B

JF - Transactions of the American Mathematical Society Series B

ER -

Rational curves on del pezzo surfaces in positive characteristic

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