Approximate Hermitian-Yang-Mills structures and semistability for Higgs bundles. II: Higgs sheaves and admissible structures

We study the basic properties of Higgs sheaves over compact K\"ahler manifolds and we establish some results concerning the notion of semistability; in particular, we show that any extension of semistable Higgs sheaves with equal slopes is semistable. Then, we use the flattening theorem to construct a regularization of any torsion-free Higgs sheaf and we show that it is in fact a Higgs bundle. Using this, we prove that any Hermitian metric on a regularization of a torsion-free Higgs sheaf induces an admissible structure on the Higgs sheaf. Finally, using admissible structures we proved some properties of semistable Higgs sheaves.Comment: 18 pages; some typos correcte

Copyright © 2007, American Society for Microbiology. All Rights Reserved. A TolC-Like Protein Is Required for Heterocyst Development in

The filamentous cyanobacterium Anabaena sp. strain PCC 7120 forms heterocysts in a semiregular pattern when it is grown on N 2 as the sole nitrogen source. The transition from vegetative cells to heterocysts requires marked metabolic and morphological changes. We show that a trimeric pore-forming outer membrane �-barrel protein belonging to the TolC family, Alr2887, is up-regulated in developing heterocysts and is essential for diazotrophic growth. Mutants defective in Alr2887 did not form the specific glycolipid layer of the heterocyst cell wall, which is necessary to protect nitrogenase from external oxygen. Comparison of the glycolipid contents of wild-type and mutant cells indicated that the protein is not involved in the synthesis of glycolipids but might instead serve as an exporter for the glycolipid moieties or enzymes involved in glycolipid attachment. We propose that Alr2887, together with an ABC transporter like DevBCA, is part of a protein export system essential for assembly of the heterocyst glycolipid layer. We designate the alr2887 gene hgdD (heterocyst glycolipid deposition protein). Gram-negative bacteria use a type I export system to transfer proteins or other molecules, like siderophores or fatty acids, to the cell surface (37, 50, 55). The proteinaceous substrates contain a C-terminal secretion signal essential an