Peculiar loci of ample and spanned line bundles

• The bad locus and the rude locus of an ample and base point free linear system on a smooth complex projective variety are introduced and studied. Polarized surfaces of small degree, or whose degree is the square of a prime, with nonempty bad loci are completely classified. Several explicit examples are offered to describe the variety of behaviors of the two loci.

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varieties

surfaces

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