• 1 Université Grenoble Alpes
• 2 Institut Fourier

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 hypersurfaces in non-Gorenstein ambiant spaces, where the convexity property fails. We extend it to any weighted projective hypersurface defined by an invertible polynomial.

• 14N35 - Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)