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Comptes Rendus. Mathématique
Algebraic geometry
On morphisms from 3 to 𝔾(1,3)
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 853-860.

Every morphism from n to 𝔾(k,m) is constant if m<n, and nonconstant morphisms from n to 𝔾(k,n) rarely appear when 0<k<n-1. In this setting, Tango proved that a morphism from n to 𝔾(1,n) is constant if n{3,5}. Here we focus on the case n=3 and show that if ϕ:𝒪 3 4 E is the surjection onto a rank 2 vector bundle E inducing a morphism φ: 3 𝔾(1,3), then h 1 (E * )1. Furthermore, a complete classification is given if equality holds.

Received:
Accepted:
Published online:
DOI: https://doi.org/10.5802/crmath.219
Classification: 14J60,  14M15,  14N05
José Carlos Sierra 1

1. Departamento de Matemáticas Fundamentales, Facultad de Ciencias, UNED, C/Juan del Rosal 10, 28040 Madrid, Spain.
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     title = {On morphisms from $\protect \mathbb{P}^3$ to $\protect \mathbb{G}(1,3)$},
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José Carlos Sierra. On morphisms from $\protect \mathbb{P}^3$ to $\protect \mathbb{G}(1,3)$. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 853-860. doi : 10.5802/crmath.219. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.219/

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