Isomorphism of Multiprojective Bundles and Projective Towers

2023/11/02 by Ashima Bansal, Supravat Sarkar, Bansal, Ashima +3 · 2 citations
Mathematics · #14M99 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2311.00999

openalex publication_date 2023/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study when two projective bundles over two arbitrary smooth projective varieties of different dimensions can be isomorphic. We show that two multi-projective bundles (fibre product of projective bundles) over different projective spaces cannot be isomorphic, except in the trivial case. We also give necessary and sufficient conditions for the top varieties of two height 3 towers of projective bundles being isomorphic, under certain assumptions.

Cited by

• Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles
• Automorphisms of punctual Hilbert schemes and symmetric powers of varieties

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