Fano manifolds of Picard number one whose co-tangent bundle is algebraically completely integrable system and its endomorphisms

2023/03/07 by Sarbeswar Pal, Pal, Sarbeswar
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2303.03665

openalex publication_date 2023/03/07 · openalex created_date 2023/03/10 · openalex updated_date 2026/07/28

Abstract

Let X be a projective Fano manifold of Picard number one, different from the projective space. There is a folklore conjecture that any non-constant endomorphism of X is an isomorphism. In the first half of this article, we will prove the folklore conjecture when the co-tangent bundle of X is algebraically completely integrable system and the tangent bundle of X is not nef. In the second half of the article, we will give examples of a collection of projective Fano manifolds of Picard rank one (different from the moduli space of vector bundles on algebraic curves) whose co-tangent bundles are algebraically completely integrable system. As applications of our main theorem and examples, in fact give alternative proofs of three major results appeared in three different articles.

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