A decomposition theorem for $\mathbb Q$-Fano K\'ahler-Einstein varieties
- Resource Type
- Working Paper
- Authors
- Druel, Stéphane; Guenancia, Henri; Păun, Mihai
- Source
- Subject
- Mathematics - Algebraic Geometry
Mathematics - Complex Variables
Mathematics - Differential Geometry
- Language
Let $X$ be a $\mathbb Q$-Fano variety admitting a K\"ahler-Einstein metric. We prove that up to a finite quasi-\'etale cover, $X$ splits isometrically as a product of K\"ahler-Einstein $\mathbb Q$-Fano varieties whose tangent sheaf is stable with respect to the anticanonical polarization. This relies among other things on a very general splitting theorem for algebraically integrable foliations. We also prove that the canonical extension of $T_X$ by $\mathscr O_X$ is semistable with respect to the anticanonical polarization.
Comment: 27 pages