3,134 research outputs found
Pluricanonical systems for 3-folds and 4-folds of general type
We explicitly find lower bounds on the volume of threefolds and fourfolds of
general type in order to have nonvanishing of pluricanonical systems and
birationality of pluricanonical maps. In the case of threefolds of large
volume, we also give necessary and sufficient conditions for the fourth
canonical map to be birational.Comment: 25 pages. Minor corrections and improved exposition. To appear in
Mathematical Proceedings of the Cambridge Philosophical Societ
Big -ample Line Bundles
A recent paper of Totaro develops a theory of -ample bundles in
characteristic 0. Specifically, a line bundle on is -ample if for
every coherent sheaf on , there exists an integer such
that implies for
. We show that a line bundle on a complex projective scheme is
-ample if and only if the restriction of to its augmented base locus is
-ample. In particular, when is a variety and is big but fails to be
-ample, then there exists a codimension 1 subscheme of such that the
restriction of to is not -ample.Comment: 9 pages, 2 pdf figure
Local positivity, multiplier ideals, and syzygies of abelian varieties
We use the language of multiplier ideals in order to relate the syzygies of
an abelian variety in a suitable embedding with the local positivity of the
line bundle inducing that embedding. This extends to higher syzygies a result
of Hwang and To on projective normality.Comment: 10 page
Some remarks on the work of Lawrence Ein
This is a write-up of introductory remarks that I made at the UIC conference
in honor of Lawrence Ein's 60th birthday. It presents an informal survey of
some of Ein's work, interspersed with stories and reminiscences
Inequalities for the Hodge numbers of irregular compact Kaehler manifolds
Based on work of R. Lazarsfeld and M. Popa, we use the derivative complex
associated to the bundle of the holomorphic p-forms to provide inequalities for
all the Hodge numbers of a special class of irregular compact Kaehler
manifolds. For 3-folds and 4-folds we give an asymptotic bound for all the
Hodge numbers in terms of the irregularity. As a byproduct, via the BGG
correspondence, we also bound the regularity of the exterior cohomology modules
of bundles of holomorphic p-forms.Comment: 15 page
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