Many cubic surfaces contain rational points

Abstract

Building on recent work of Bhargava--Elkies--Schnidman and Kriz--Li, we produce infinitely many smooth cubic surfaces defined over the field of rational numbers that contain rational points.

23 pages; minor edits and added new remark (Remark 2.1) following an argument of Jahnel

References in corpus (3)

• The average size of the 3-isogeny Selmer groups of elliptic curves $y^2=x^3+k$
• Obstructions to the Hasse principle in families
• Heegner points at Eisenstein primes and twists of elliptic curves

Cited by in corpus (3)

• The average size of the 3-isogeny Selmer groups of elliptic curves $y^2=x^3+k$
• The mean number of 2-torsion elements in the class groups of $n$-monogenized cubic fields
• On the proportion of locally soluble superelliptic curves