Blow-ups of Algebraically Elliptic Manifolds

Prove that the blow-up of an algebraically elliptic manifold along any algebraic submanifold is algebraically elliptic.

Background

The authors review positive results showing that various blow-ups preserve strong dominability and related properties, and that blow-ups of uniformly rational compact manifolds are algebraically elliptic. They note broad evidence suggesting stability of algebraic ellipticity under blow-ups.

Despite this evidence, the general statement that blow-ups of algebraically elliptic manifolds remain algebraically elliptic has not yet been proved, leaving a key birational aspect of algebraic ellipticity open.