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 K
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