Intrinsic mirrors for minimal adjoint orbits and categories of singularities

Abstract

I discuss mirrors of Landau-Ginzburg models formed by a minimal semisimple adjoint orbit of $\mathfrak{sl}(n)$ together with a potential obtained via the Cartan-Killing form. I show that the Landau-Ginzburg models produced by the Gross-Siebert recipe give precisely the objects of the desired mirrors. It is known that Landau-Ginzburg model $LG(2)$ over the semisimple adjoint orbit of $\mathfrak{sl}(2)$ does not have projective mirrors. I prove Homological Mirror Symmetry for $LG(2)$ by constructing a Landau-Ginzburg mirror and showing that its Orlov category of singularities is equivalent to $Fuk(LG(2))$.

With figures and additional remark 8 as requested by the referee

References in corpus (2)

• Triangulated categories of singularities and D-branes in Landau-Ginzburg models
• Vector bundles near negative curves: moduli and local Euler characteristic

Cited by in corpus (1)

• Birationally equivalent Landau-Ginzburg models on cotangent bundles and adjoint orbits