The algebra of symmetric tensors on smooth projective varieties

2023/09/22 by Arnaud Beauville, Beauville, Arnaud, Liu, Jie
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2309.12888

openalex publication_date 2023/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We discuss in this note the algebra H⁰(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.

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