Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles

TL;DR

This paper characterizes when multiprojective bundles and symmetric powers of projective bundles over projective spaces are isomorphic, and describes their automorphisms, advancing understanding of their structural properties.

Contribution

It provides criteria for isomorphisms between multiprojective bundles and symmetric powers, and details their automorphism groups, offering new insights into their geometric structure.

Findings

Criteria for isomorphism of multiprojective bundles

Conditions for isomorphism of symmetric powers

Descriptions of automorphism groups

Abstract

We describe when two multiprojective bundles (fibre products of projective bundles over the same base) over projective spaces are isomorphic as abstract varieties. We also describe when two relative symmetric powers of projective bundles over projective spaces are isomorphic. Finally, we describe the automorphisms of multiprojective bundles and relative symmetric powers of projective bundles over projective spaces.