Counting rational curves equivariantly

Abstract: This talk will be a friendly introduction to using topological invariants in enumerative geometry and how one might use equivariant homotopy theory to answer enumerative questions under the presence of a finite group action. Recent work with Kirsten Wickelgren (Duke) defines a global and local degree in stable equivariant homotopy theory that can be used to compute the equivariant Euler characteristic and Euler number. I will discuss an application to counting orbits of rational plane cubics through an invariant set of 8 points in general position under a finite group action on $\mathbb{C}\mathbb{P}^2$, valued in the representation ring and Burnside ring. This recovers a signed count of real rational cubics when $\mathbb{Z}/2$ acts on $\mathbb{C}\mathbb{P}^2$ by complex conjugation.

algebraic geometryalgebraic topology

Audience: researchers in the topic

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Boston University Number Theory Seminar