On integral points of some Fano Threefolds and their Hilbert schemes of lines and conics

2022/11/07 by Pietro Corvaja, Corvaja, Pietro, Francesco Zucconi +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Analytic Number Theory Research

paper · pdf · doi:10.48550/arxiv.2211.03397

Abstract

Let X^o=\mathbb P³∖ D where D is the union of two quadrics such that their intersection contains a smooth conic, or the union of a smooth quadric surface and two planes, or the union of a smooth cubic surface V and a plane Π such that the intersection V∩Π contains a line. In all these cases we show that the set of integral points of X^o is potentially dense. We apply the above results to prove that integral points are potentially dense in some log-Fano or in some log-Calabi-Yau threefold.

Related

• Integral points on conic log K3 surfaces
• Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds
• Integral points of bounded height on a log Fano threefold
• Lines, conics, and all that
• Codimension two integral points on some rationally connected threefolds are potentially dense