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.

Correction to: A characterization of symplectic Grassmannians (Mathematische Zeitschrift, (2017), 286, 3-4, (1421-1433), 10.1007/s00209-016-1807-6) / Occhetta, G.; Sola Conde, L. E.; Watanabe, K.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 292:1-2(2019), pp. 569-570. [10.1007/s00209-019-02230-y]

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

Occhetta G.;Sola Conde L. E.;
2019

Abstract

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.
1-2
Occhetta, G.; Sola Conde, L. E.; Watanabe, K.
Correction to: A characterization of symplectic Grassmannians (Mathematische Zeitschrift, (2017), 286, 3-4, (1421-1433), 10.1007/s00209-016-1807-6) / Occhetta, G.; Sola Conde, L. E.; Watanabe, K.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - 292:1-2(2019), pp. 569-570. [10.1007/s00209-019-02230-y]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/240180
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