181 research outputs found
On the cohomology of pseudoeffective line bundles
The goal of this survey is to present various results concerning the
cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and
related properties of their multiplier ideal sheaves. In case the curvature is
strictly positive, the prototype is the well known Nadel vanishing theorem,
which is itself a generalized analytic version of the fundamental
Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested
here in the case where the curvature is merely semipositive in the sense of
currents, and the base manifold is not necessarily projective. In this
situation, one can still obtain interesting information on cohomology, e.g. a
Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a
surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his
PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing
theorem that depends on the concept of numerical dimension of a given
pseudoeffective line bundle. The proof of these results depends in a crucial
way on a general approximation result for closed (1,1)-currents, based on the
use of Bergman kernels, and the related intersection theory of currents.
Another important ingredient is the recent proof by Guan and Zhou of the strong
openness conjecture. As an application, we discuss a structure theorem for
compact K{\"a}hler threefolds without nontrivial subvarieties, following a
joint work with F.Campana and M.Verbitsky. We hope that these notes will serve
as a useful guide to the more detailed and more technical papers in the
literature; in some cases, we provide here substantially simplified proofs and
unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the
Abel Symposium, Trondheim, July 201
Fractional deuteration applied to biomolecular solid-state NMR spectroscopy
Solid-state Nuclear Magnetic Resonance can provide detailed insight into structural and dynamical aspects of complex biomolecules. With increasing molecular size, advanced approaches for spectral simplification and the detection of medium to long-range contacts become of critical relevance. We have analyzed the protonation pattern of a membrane-embedded ion channel that was obtained from bacterial expression using protonated precursors and D2O medium. We find an overall reduction of 50% in protein protonation. High levels of deuteration at Hα and Hβ positions reduce spectral congestion in (1H,13C,15N) correlation experiments and generate a transfer profile in longitudinal mixing schemes that can be tuned to specific resonance frequencies. At the same time, residual protons are predominantly found at amino-acid side-chain positions enhancing the prospects for obtaining side-chain resonance assignments and for detecting medium to long-range contacts. Fractional deuteration thus provides a powerful means to aid the structural analysis of complex biomolecules by solid-state NMR
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