Potential density of rational points for K3 surfaces over function fields

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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Sections of Calabi-Yau threefolds with K3 fibration

2014

Trans. Amer. Math. Soc.

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We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the Néron-Severi group generated by these sections is not finitely generated. This also gives examples of K3 surfaces over the function field F of a complex curve with Zariski dense F -rational points, whose geometric model is Calabi-Yau.

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Potential density of rational points for K3 surfaces over function fields

Abstract: Abstract. We give examples of non-isotrivial K3 surfaces over complex function fields with Zariski-dense rational points and Néron-Severi rank one.

Cited by 5 publications

References 17 publications

Geometry Over Nonclosed Fields

Geometry Over Nonclosed Fields

Rational curves on del Pezzo surfaces in positive characteristic

Sections of Calabi-Yau threefolds with K3 fibration

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