Algebraic vector bundles on punctured affine spaces and smooth quadrics

TL;DR

This paper constructs examples of algebraic vector bundles on punctured affine spaces that become isomorphic when pulled back to smooth quadrics, highlighting differences in bundle structures across these varieties.

Contribution

It provides explicit examples of non-isomorphic bundles on punctured affine spaces with isomorphic pullbacks to smooth quadrics, advancing understanding of vector bundle behavior.

Findings

Constructed non-isomorphic bundles on punctured affine spaces

Demonstrated isomorphism of pullbacks to smooth quadrics

Enhanced understanding of algebraic vector bundle structures

Abstract

We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.