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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…
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…
Bitangents to symmetric quartics
Candace Bethea, Thomas Brazelton
Recall that a non-singular planar quartic is a canonically embedded non-hyperelliptic curve of genus three. We say such a curve is symmetric if it admits non-trivial automorphisms.…
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…
An Introduction to -Enumerative Geometry
Thomas Brazelton
We provide an expository introduction to -enumerative geometry, which uses the machinery of -homotopy theory to enrich classical enumerative geometry qu…