Date/Time
Date(s) - 23/09/2025
11:30 am - 12:30 pm

Speaker: Tariq Syed (Heinrich-Heine-Universität Düsseldorf)
Research area(s): algebraic geometry and commutative algebra

Location: Hamilton Hall, Room 312

Title: On algebraic vector bundles of rank 2 over smooth affine fourfolds

Abstract: The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds over algebraically closed fields is a notoriously difficult problem. In contrast to the situation in lower dimensions, rank 2 bundles over smooth affine fourfolds are no longer uniquely determined up to isomorphism by their Chern classes. In this talk, we survey classification results in low dimensions and analyze the cohomological obstructions for the set of isomorphism classes of rank 2 bundles with prescribed Chern classes over a fixed smooth affine fourfold to be finite (resp. a singleton). This enables us in many cases to enumerate isomorphism classes of rank 2 bundles with prescribed Chern classes; we can even completely classify rank 2 bundles over some concrete smooth affine fourfolds. The talk is based on joint work with Thomas Brazelton and Morgan Opie.