The algebra of symmetric tensors on smooth projective varieties

Abstract

We discuss in this note the algebra H^0(X, Sym*TX) for a smooth complex projective variety X . We compute it in some simple examples, and give a sharp bound on its Krull dimension. Then we propose a conjectural characterization of non-uniruled projective manifolds with pseudo-effective tangent bundle.

Minor changes. To appear in Science China Mathematics, volume in memory of Gang Xiao