Counting joints in vector spaces over arbitrary fields

Abstract

We give a proof of the "folklore" theorem that the Kaplan--Sharir--Shustin/Quilodrán result on counting joints associated to a family of lines holds in vector spaces over arbitrary fields, not just the reals. We also discuss a distributional estimate on the multiplicities of the joints in the case that the family of lines is sufficiently generic.

Not intended for publication. References added and other minor edits in this version

References in corpus (2)

• The joints problem in R^n
• Discrete analogues of Kakeya problems

Cited by in corpus (3)

• On the joints problem with multiplicities
• Joints of varieties
• A proof of the Multijoints Conjecture and Carbery's generalization