2024/03/26 by Andrés Jaramillo Puentes, Puentes, Andrés Jaramillo · 1 citation
Computer Science · Mathematics · #14G27 (Secondary) #14N10 #14N35 (Primary) 14T25 #Advanced Combinatorial Mathematics #Advanced Graph Theory Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2403.17681
openalex publication_date 2024/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.