• Corpus ID: 234771715

On the big quantum cohomology of Fano complete intersections.

@article{Hu2015OnTB,
  title={On the big quantum cohomology of Fano complete intersections.},
  author={Xiaowen Hu},
  journal={arXiv: Algebraic Geometry},
  year={2015}
}

• Xiaowen Hu
• Published 15 January 2015
• Mathematics
• arXiv: Algebraic Geometry

For smooth complete intersections in the projective spaces, we make use of the deformation invariance of Gromov-Witten invariants and results in classical invariant theory to study the symmetric reduction of the WDVV equation by the monodromy groups. We discuss to what extent the quantum cohomology involving primitive cohomology classes can be determined. In particular, we obtain a reconstruction theorem for (i) genus zero Gromov-Witten invariants of cubic hypersurfaces and odd dimensional complete intersection of two quadrics and (ii) genus zero Gromov-Witten invariants with at most 4 primitive insertions for all Fano complete intersections of dimension at least 3. By the way, we obtain a complete description of the cohomology ring of the Fano variety of lines on smooth cubic hypersurfaces.