Refined Riemann-Roch for degenerations of Calabi-Yau manifolds and a mirror symmetry-conjecture

2023/03/28 Tue 10:00 - 11:00
Dennis Eriksson
Charmers University

In semi-recent joint work (w. Gerard Freixas and Christophe Mourougane) we proved a mirror symmetry-statement for genus one Gromov-Witten invariants of Calabi-Yau hypersurfaces in projective space, building upon ideas of Ken-Ichi Yoshikawa and his collaborators. A central tool was a reformulation of the conjecture, originally posed by string theorists, using a metric version of the Grothendieck-Riemann-Roch theorem. In this talk, I will focus on a formulation of a more mathematical version of the conjecture, together with a list of examples where it is verified. There are two main ingredients, namely the limit mixed Hodge structure of a maximally degenerate family, and a lifting of the (codimension 1)-version of the Grothendieck-Riemann-Roch theorem to the level of line bundles. The latter ingredient is ongoing joint work Gerard Freixas.