English

The mirror Lagrangian cobordism for the Euler exact sequence

Algebraic Geometry 2021-12-14 v2 Symplectic Geometry

Abstract

For X=PnX = \mathbb{P}^n the Euler sequence is given by 0ΩPn1OPnn+1(1)OPn0 0 \rightarrow \Omega^1_{\mathbb{P}^n} \rightarrow \mathcal{O}_{\mathbb{P}^n}^{n+1}(-1) \rightarrow \mathcal{O}_{\mathbb{P}^n} \rightarrow 0 We describe the Lagrangian cobordism corresponding to this sequence via mirror symmetry, in the sense of Biran-Cornea. In particular, we describe the mirror Lagrangian of the cotangent sheaf ΩPn1Db(Pn)\Omega^1_{\mathbb{P}^n} \in \mathcal{D}^b(\mathbb{P}^n) in the mirror Fukaya category Fuk(UΔ)Fuk(U_{\Delta}).

Keywords

Cite

@article{arxiv.2112.03058,
  title  = {The mirror Lagrangian cobordism for the Euler exact sequence},
  author = {Yochay Jerby},
  journal= {arXiv preprint arXiv:2112.03058},
  year   = {2021}
}
R2 v1 2026-06-24T08:05:59.131Z