Base divisors of big and nef line bundles on irreducible symplectic varieties
Annales de l'Institut Fourier, Online first, 25 p.

Under some conditions on the deformation type, which we expect to be satisfied for arbitrary irreducible symplectic varieties, we describe which big and nef line bundles on irreducible symplectic varieties have base divisors. In particular, we show that such base divisors are always irreducible and reduced. This is applied to understand the behaviour of divisorial base components of big and nef line bundles under deformations and for K3 [n] -type and Kum n -type.

Nous décrivons quels fibrés en droites gros et nefs, sur des variétés symplectiques irréductibles, ont des diviseurs de base, sous certaines conditions relatives au type de déformation dont nous nous attendons à ce qu’elles soient vraies pour toutes les variétés symplectiques irréductibles. En particulier, nous montrons que de tels diviseurs de base sont toujours réduits et irréductibles. Nous appliquons ces résultats pour comprendre le comportement après déformation des diviseurs de base des fibrés en droites gros et nefs. Nous terminons en donnant une déscription très explicite pour les variétés de types K3 [n] et Kum n .

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Accepted:
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DOI: 10.5802/aif.3530
Classification: 14M99
Keywords: Irreducible symplectic varieties, hyperkähler manifolds, base divisors, Fujita’s conjecture
Rieß, Ulrike 1

1 ETH Zürich Institute for Theoretical Studies Clausisusstrasse 47 8092 Zürich (Switzerland)
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Rieß, Ulrike. Base divisors of big and nef line bundles on irreducible symplectic varieties. Annales de l'Institut Fourier, Online first, 25 p.

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