R-matrix reconstruction conjecture for the intersection of two quadrics

Let XX be the complete intersection of two quadric hypersurfaces in CP5\mathbb{CP}^5, and let Σ2\Sigma_2 be a genus 22 surface. Suppose an R-matrix relates the two splittings of the quantum cohomology induced by the cyclic open-closed map and by the canonical Gromov–Witten splitting. R-matrix reconstruction conjecture. This R-matrix recovers all, including higher-genus, Gromov–Witten invariants of XX from the genus 00, 33-point invariants of XX and the all-genus Gromov–Witten invariants of Σ2\Sigma_2. This is a concrete reconstruction claim in the paper's example of the intersection of two quadrics; the source does not report a resolution.

Sources & referencesView supporting material

Primary source

Kai Hugtenburg, “The cyclic open-closed map, u-connections and R-matrices”, arXiv:2205.13436 (2024).

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