Non-solidity of uniruled varieties

TL;DR

This paper investigates conditions under which uniruled varieties are non-solid, supporting a conjecture about Fano 3-folds, and provides explicit birational links for high codimension Fano 3-folds.

Contribution

It offers new criteria for non-solidity of uniruled varieties and constructs explicit birational links for certain Fano 3-folds.

Findings

Identifies conditions for non-solidity in uniruled varieties

Supports the conjecture on Fano 3-folds solidity

Provides explicit birational links for high codimension Fano 3-folds

Abstract

We give conditions for a uniruled variety of dimension at least 2 to be non-solid. This study provides further evidence to a conjecture by Abban and Okada on the solidity of Fano 3-folds. To complement our results we write explicit birational links from Fano 3-folds of high codimension embedded in weighted projective spaces.