1,181 research outputs found
Nakamaye's theorem on log canonical pairs
We generalize Nakamaye's description, via intersection theory, of the
augmented base locus of a big and nef divisor on a normal pair with
log-canonical singularities or, more generally, on a normal variety with non-lc
locus of dimension at most 1. We also generalize
Ein-Lazarsfeld-Mustata-Nakamaye-Popa's description, in terms of valuations, of
the subvarieties of the restricted base locus of a big divisor on a normal pair
with klt singularities.Comment: v2: We removed, in the introduction, the phrase about Choi's papers,
as he uses Nakamaye's theorem in the semiample case. Updated references. v3:
added reference to Ambro's "Quasi-log varieties". v4: improved exposition in
sections 1, 2 and 4; slightly corrected the statement of Lemma 3.
Brill-Noether theory of curves on Enriques surfaces, II. The Clifford index
We complete our study of linear series on curves lying on an Enriques surface
by showing that, with the exception of smooth plane quintics, there are no
exceptional curves on Enriques surfaces, that is, curves for which the Clifford
index is not computed by a pencil
Augmented base loci and restricted volumes on normal varieties
We extend to normal projective varieties defined over an arbitrary
algebraically closed field a result of Ein, Lazarsfeld, Musta\c{t}\u{a},
Nakamaye and Popa characterizing the augmented base locus (aka non-ample locus)
of a line bundle on a smooth projective complex variety as the union of
subvarieties on which the restricted volume vanishes. We also give a proof of
the folklore fact that the complement of the augmented base locus is the
largest open subset on which the Kodaira map defined by large and divisible
multiples of the line bundle is an isomorphism.Comment: 7 pages. v2: we made a small modification of the statement of Lemma
2.4, a few minor corrections and updated reference
- …