The mirror Lagrangian cobordism for the Euler exact sequence

Abstract

For $X={\mathbb{P}}^n$ the Euler sequence is given by $$0\to {\Omega }_{{\mathbb{P}}^n}^1\to {\mathcal{O}}_{{\mathbb{P}}^n}^{n+1}(-1)\to {\mathcal{O}}_{{\mathbb{P}}^n}\to 0$$ 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 ${\Omega }_{{\mathbb{P}}^n}^1\in {\mathcal{D}}^b({\mathbb{P}}^n)$ in the mirror Fukaya category $Fuk(U_{\Delta })$.