Geometry and Topology: Hodge-Gromov-Witten theory

  • Date: –15:00
  • Location: Ångströmlaboratoriet, Lägerhyddsvägen 1 64119
  • Lecturer: Jérémy Guéré (Université Grenoble Alpes)
  • Organiser: Matematiska institutionen
  • Contact person: Georgios Dimitroglou Rizell
  • Seminarium

Abstract: Hodge-Gromov-Witten theory of a smooth projective variety X deals with the cap product of the virtual fundamental cycle on the moduli space of stable maps to X with the Euler class of the Hodge vector bundle. I recently studied its deformation invariance to singular varieties, allowing explicit computations in many cases. An important application of my theorem is a calculation of genus-zero GW invariants for some hypersurfaces in weighted projective spaces which do not satisfy the so-called convexity property. It is a first step towards a mirror symmetry statement for these hypersurfaces.
In a second part of the talk, I will describe my plan towards a calculation of GW invariants of the quintic hypersurface in P^4. It is based on a theorem Costello proved in 2003 expressing genus-g GW invariants of a projective variety X in terms of genus-0 GW invariants of the (g+1)-st symmetric power of X.