An analogue of Dubrovin's conjecture

Fumihiko Sanda, Yota Shamoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call “mutation systems”. Given such a Fano manifold X, one of the structures is given by the Stokes structure of the quantum connection of X, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on X. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.

Original languageEnglish
Pages (from-to)621-682
Number of pages62
JournalAnnales de l'Institut Fourier
Volume70
Issue number2
DOIs
Publication statusPublished - 2020
Externally publishedYes

Keywords

  • Fano manifolds
  • Mirror symmetry
  • Quantum cohomologies
  • Stokes matrix

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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