Modified virtual localization for complete intersections in algebraic GKM manifolds

Let an algebraic GKM manifold be a smooth algebraic variety equipped with an algebraic torus action having isolated fixed points and finitely many one-dimensional orbits, and let a complete intersection be given in such a manifold. The modified virtual localization procedure is obtained by incorporating correction terms into the localization contributions associated with higher-genus vertices, as in the genus-one construction for Calabi–Yau hypersurfaces.

Modified localization conjecture. An analog of the theorem asserting that modified virtual localization computes the genus-one Gromov–Witten invariants of a Calabi–Yau hypersurface holds for complete intersections in algebraic GKM manifolds.

This conjecture extends the modified localization formula from complete intersections in projective space to complete intersections in algebraic GKM manifolds. The source leaves its precise formulation open.