We prove that the refined BPS invariants for local P² satisfy an asymptotic product formula as conjectured by Kononov--Pi--Shen. Combined with the P⊃ C result of Maulik--Shen--Yin obtained from a theory of Fourier transform, we prove the $P=C$ conjecture for degree d curves on P² in cohomological degrees ≤ d+1.
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Pi et al. (2024) studied this question.
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