Correction to: A characterization of symplectic Grassmannians (Mathematische Zeitschrift, (2017), 286, 3-4, (1421-1433), 10.1007/s00209-016-1807-6)

We thank Jun-Muk Hwang for pointing out that the homomorphism of algebraic groups η : GL(F ∨2,x )Q ∨x → GL(T X,x ) has a nontrivial kernel (isomorphic to Z 2 ), preventing us from defining, in Section 3.3, the vector bundles Q ∨ , F ∨1 ,F ∨2 . However, the main Theorem of the paper may still be proved by slightly modifying our arguments as follows. 1. In Section 3.3, instead of defining the vector bundles Q ∨ ,F ∨1 , F ∨2 over X, we may only define the corresponding projective bundles Z, u 1 and u 2 over X, and vector bundles G, HG over U1, whose projectivizations give U and HU, fitting in a sequence: 0 → K → G → HG → 0, with K a line bundle. On the other hand, the desired vector bundles Q ∨ ,F ∨1 , F ∨2 may still be constructed over a rational curve l of the family M. By choosing an appropriate twist, they fit in the commutative diagram.