Mathematics > Algebraic Geometry
[Submitted on 13 Jul 2018]
Title:Base divisors of big and nef line bundles on irreducible symplectic varieties
View PDFAbstract: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.
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