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A Wall Crossing Formula for Motivic Enumerative Invariants
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abstract
We prove an analog of the wall crossing formula for Welschinger invariants relating the difference of signed curve counting of real curves passing through configurations that differ by a pair of complex conjugated points, and a correspondence Welschinger invariant of the blow up. We prove this analogue for the motivic count of rational curves of fixed degree passing through a generic configuration of points, counted with a motivic multiplicity in the Grothendieck-Witt ring of a base field, extending the notions in the correspondence theorem between motivic invariants for $k$-rational point conditions and tropical curves. We use this formula to compute the degree 4 motivic enumerative invariants of the projective plane counting curves passing through configurations of points defined over quadratic extensions of a base field.
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Cited by 1 Pith paper
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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.
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