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

Moduli and Algebraic Cycles

30 November 13:15 - 14:15

Dennis Eriksson - Chalmers/University of Gothenburg

In 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. The original conjecture was formulated by string theorists. A central tool was a reformulation of the conjecture, using an metric version of the Riemann-Roch. 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 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.

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John Christian Ottem
University of Oslo
Dan Petersen
Stockholm University
David Rydh
KTH Royal Institute of Technology


Dan Petersen


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