On the triviality of the direct image of coherent sheaves

2026/01/28 by Indranil Biswas, Jagadish Pine
Mathematics · #Algebraic Geometry and Number Theory #Mathematical and Theoretical Analysis #advanced mathematical theories #math.AG

paper · pdf · doi:10.1016/j.jpaa.2026.108355

openalex publication_date 2026/07/22 · openalex created_date 2026/07/23 · openalex updated_date 2026/07/28

Abstract

Let π : X \longrightarrow Y be a finite morphism of projective varieties defined over an algebraically closed field of characteristic zero. We study the necessary and sufficient criteria for π such that there exists a coherent sheaf E on X whose direct image π_*E is a trivial vector bundle on Y of positive rank. When X is smooth, and Y is Cohen-Macaulay, such a coherent sheaf is necessarily locally free. We show that the existence of such a coherent sheaf E is guided by the properties of the branching divisor of π. When the covering π : X \longrightarrow Y is admissible abelian Galois, we give a complete answer. As an application, it is shown that every smooth admissible abelian Galois covering of ℙⁿ supports an Ulrich bundle.

Citations

• Ulrich bundles on cyclic coverings of projective spaces
• Ulrich bundles on double covers of projective spaces
• Non-normal abelian covers
• Linear maximal Cohen-Macaulay modules over strict complete intersections

Cited by

• Ulrich bundles on cyclic coverings of projective spaces

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