Universal unramified cohomology of cubic fourfolds containing a plane

TL;DR

This paper proves that for very general complex cubic fourfolds containing a plane, the third unramified cohomology group is universally trivial, advancing understanding of their algebraic and geometric properties.

Contribution

It establishes the universal triviality of the third unramified cohomology for a broad class of cubic fourfolds, using advanced cohomological techniques.

Findings

Third unramified cohomology group is universally trivial for these fourfolds

Uses results on unramified cohomology of quadrics by Kahn, Rost, and Sujatha

Provides new insights into the algebraic structure of cubic fourfolds containing a plane

Abstract

We prove the universal triviality of the third unramified cohomology group of a very general complex cubic fourfold containing a plane. The proof uses results on the unramified cohomology of quadrics due to Kahn, Rost, and Sujatha.