New examples of geometrically special varieties: K3 surfaces, Enriques surfaces, and algebraic groups

2025/02/13 by Finn Bartsch, Bartsch, Finn · 1 citation
Computer Science · Mathematics · #14G25 (Primary) 14J28 #14L99 #32Q99 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2502.09400

openalex publication_date 2025/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We verify that elliptic K3 surfaces and algebraic groups have many rational points over function fields, i.e., they are geometrically special in the sense of Javanpeykar-Rousseau. We also show that under additional assumptions, this geometric specialness persists under removal of closed subsets of codimension at least two.

Cited by

• Hilbert properties of varieties

Related

• K3 surfaces, rational curves, and rational points
• K3 surfaces with Picard number one and infinitely many rational points
• Rational curves on elliptic K3 surfaces
• Complex surfaces with many algebraic structures
• Rational surfaces with a non-arithmetic automorphism group