Projective center point and Tverberg theorems

TL;DR

This paper introduces projective versions of the center point and Tverberg theorems, unifying various known results and presenting new findings on measure partitioning in projective space.

Contribution

It provides a unified theorem that generalizes multiple Tverberg-type results and introduces novel results in measure partitioning within projective geometry.

Findings

Unified theorem encompassing various Tverberg results

New results on measure partitioning in projective space

Interpolation between original and dual theorems

Abstract

We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. Furthermore we give a common generalization of these and many other known (transversal, constraint, dual, and colorful) Tverberg type results in a single theorem, as well as some essentially new results about partitioning measures in projective space.