A correspondence theorem equates quadratically enriched algebraic curve counts with conjugate point conditions to tropical counts with double point conditions, and a floor diagram algorithm computes them.
Power structures on the Grothendieck--Witt ring and the motivic Euler characteristic
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abstract
For $k$ a field, we construct a power structure on the Grothendieck--Witt ring of $k$ which has the potential to be compatible with symmetric powers of varieties and the motivic Euler characteristic. We then show this power structure is compatible with the power structure when we restrict to varieties of dimension $0$.
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Quadratically Enriched Plane Curve Counting via Tropical Geometry
A correspondence theorem equates quadratically enriched algebraic curve counts with conjugate point conditions to tropical counts with double point conditions, and a floor diagram algorithm computes them.