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

TL;DR

This paper completes the genus 0 Gromov-Witten theory for even-dimensional complete intersections of two quadrics by computing a previously undetermined invariant using degeneration techniques.

Contribution

It provides the final step in determining all genus 0 Gromov-Witten invariants for these special varieties, filling a gap left by prior geometric methods.

Findings

Computed the missing Gromov-Witten invariant using degeneration formula.

Established the full genus 0 Gromov-Witten theory for these complete intersections.

Extended understanding of Gromov-Witten invariants beyond invariant cases.

Abstract

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 genus~0 Gromov-Witten theory of $X$ was studied by Xiaowen Hu. He used geometric arguments and the WDVV equation to compute all genus~0 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.