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Local multiplicities for an equivariantly enriched non-transverse Bézout's theorem
Candace Bethea, Charanya Ravi
We introduce the degree and local degree in equivariant motivic homotopy theory for the purpose of studying equivariant enumerative problems over general fields. Given a finite, ta…
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…
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.…
An enriched count of nodal orbits in an invariant pencil of conics
Candace Bethea
This work gives an equivariantly enriched count of nodal orbits in a general pencil of plane conics that is invariant under a linear action of a finite group on . Th…
An Example of Wild Ramification in an Enriched Riemann-Hurwitz Formula
Candace Bethea, Jesse Leo Kass, Kirsten Wickelgren
M. Levine proved an enrichment of the classical Riemann-Hurwitz formula to an equality in the Grothendieck-Witt group of quadratic forms. In its strongest form, Levine's theorem in…