References & Citations
Mathematics > Algebraic Geometry
Title: A Wall Crossing Formula for Motivic Enumerative Invariants
(Submitted on 26 Mar 2024 (v1), last revised 19 Apr 2024 (this version, v2))
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.
Submission history
From: Andrés Jaramillo Puentes [view email][v1] Tue, 26 Mar 2024 13:12:35 GMT (710kb,D)
[v2] Fri, 19 Apr 2024 00:17:14 GMT (710kb,D)
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