Let (X, L) be a smooth polarized variety of dimension n. Let A ∈ |L| be an effective irreducible divisor, and let Σ be the singular locus of A. We assume that Σ is a smooth subvariety of dimension k ≥ 2, and codimension c ≥ 3, consisting of non-degenerate quadratic singularities. We study positivity conditions for adjoint bundles K<inf>X</inf> +tL with t ≥ n-3. Several explicit examples motivate the discussion.

Adjunction and singular loci of hyperplane sections

BELTRAMETTI, MAURO CARLO;
2015-01-01

Abstract

Let (X, L) be a smooth polarized variety of dimension n. Let A ∈ |L| be an effective irreducible divisor, and let Σ be the singular locus of A. We assume that Σ is a smooth subvariety of dimension k ≥ 2, and codimension c ≥ 3, consisting of non-degenerate quadratic singularities. We study positivity conditions for adjoint bundles KX +tL with t ≥ n-3. Several explicit examples motivate the discussion.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/862478
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