no. 6
Multipoint Okounkov bodies
[Corps d’Okounkov à plusieurs points]
Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2595-2646.

Étant donné un grand fibré en droites gros L sur une variété projective X et le choix de N≥1 points différents sur X, on donne une nouvelle construction de N corps d’Okounkov qui donne des informations géométriques importantes sur (L→X;p 1 ,⋯,p N ) comme, par example, le volume de L, la constante de Seshadri de L aux points p 1 ,⋯,p N et la possibilité de construire des « Kähler packings » centrés en p 1 ,⋯,p N . Les cas des variétés toriques et des surfaces sont examinés en détail.

Starting from the data of a big line bundle L on a projective manifold X with a choice of N≥1 different points on X we provide a new construction of N Okounkov bodies that encode important geometric features of (L→X;p 1 ,⋯,p N ) such as the volume of L, the (moving) multipoint Seshadri constant of L at p 1 ,⋯,p N , and the possibility to construct Kähler packings centered at p 1 ,⋯,p N . Toric manifolds and surfaces are examined in detail.

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DOI : 10.5802/aif.3462
Classification : 14C20, 32Q15, 57R17
Keywords: Okounkov body, Seshadri constant, packings problem, projective manifold, ample line bundle.
Mot clés : Corps d’Okounkov, constante de Seshadri, problème du « packing », variété projective, fibré en droite ample. 
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Trusiani, Antonio. Multipoint Okounkov bodies. Annales de l'Institut Fourier, Tome 71 (2021) no. 6, pp. 2595-2646. doi : 10.5802/aif.3462. http://www.numdam.org/articles/10.5802/aif.3462/

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