  We determine the all-genus Hodge-Gromov-Witten theory of a smooth
hypersurface in weighted projective space defined by a chain or loop
polynomial. In particular, we obtain the first genus-zero computation of
Gromov-Witten invariants for non-Gorenstein hypersurfaces, where the convexity
property fails. We eventually extend it to any weighted projective hypersurface
defined by an invertible polynomial.
