Genus~0 Gromov-Witten theory of even dimensional complete intersections of two quadrics: the final step

Even dimensional complete intersections $X$ of two quadrics in projective space are exceptional from the point of view of the Gromov-Witten theory: they are (together with qubic surfaces) the only complete intersections whose Gromov-Witten theory is not invariant under the full orthogonal or symplectic group acting on the primitive cohomology. The genus0 Gromov-Witten theory of $X$ was studied by Xiaowen Hu. He used geometric arguments and the WDVV equation to compute all genus0 correlators except one, which cannot be determined by his methods. In this paper we compute the remaining Gromov-Witten invariant of $X$ using Jun Li’s degeneration formula.

💡 Research Summary

The paper addresses a long‑standing gap in the genus‑0 Gromov‑Witten theory of even‑dimensional smooth complete intersections of two quadrics in projective space. Such varieties X⊂ℙ^{m+2} (with even dimension m≥4) are exceptional because their primitive cohomology is not acted on by the full orthogonal or symplectic group; the monodromy group is finite. Xiaowen Hu (2021) computed all genus‑0 correlators using geometric arguments and the WDVV equation, except for a single invariant involving m+3 primitive insertions: \