3 papers
math.AG2025
Monodromy in the space of symmetric cubic surfaces with a line
Thomas Brazelton, Sidhanth Raman
We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic…
math.AG2025
The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants
Candace Bethea, Thomas Brazelton
Enumerative geometry, the art and science of counting geometric objects satisfying geometric conditions, has seen a resurgence of activity in recent years due to an influx of new t…
math.AG2025
On algebraic vector bundles of rank over smooth affine fourfolds
Thomas Brazelton, Morgan Opie, Tariq Syed
The classification of algebraic vector bundles of rank 2 over smooth affine fourfolds is a notoriously difficult problem. Isomorphism classes of such vector bundles are not uniquel…