An analogue of Dubrovin's conjecture

Fumihiko Sanda, Yota Shamoto

研究成果: Article査読

抄録

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.

本文言語English
ページ(範囲)621-682
ページ数62
ジャーナルAnnales de l'Institut Fourier
70
2
DOI
出版ステータスPublished - 2020
外部発表はい

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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