Birationality of \'etale morphisms via surgery

We use a counting argument and surgery theory to show that if $D$ is a sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a $d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (however all degrees $d > 1$ are possible if $F$ fails to be a local diffeomorphism at even a single point). In particular, any \'etale morphism $F:X \to \Bbb C^n$ of algebraic varieties which covers away from such a hypersurface $D$ must be birational.Comment: 17 pages. Replaced to add further references and make language more consistent with the literatur

On the imaging of electron transport in semiconductor quantum structures by scanning-gate microscopy: successes and limitations

This paper presents a brief review of scanning-gate microscopy applied to the imaging of electron transport in buried semiconductor quantum structures. After an introduction to the technique and to some of its practical issues, we summarise a selection of its successful achievements found in the literature, including our own research. The latter focuses on the imaging of GaInAs-based quantum rings both in the low magnetic field Aharonov-Bohm regime and in the high-field quantum Hall regime. Based on our own experience, we then discuss in detail some of the limitations of scanning-gate microscopy. These include possible tip induced artefacts, effects of a large bias applied to the scanning tip, as well as consequences of unwanted charge traps on the conductance maps. We emphasize how special care must be paid in interpreting these scanning-gate images.Comment: Special issue on (nano)characterization of semiconductor materials and structure

Atypical presentation of pellucid marginal degeneration: case report

The authors report an unusual clinical presentation of pellucid marginal degeneration with 360º peripheral corneal thinning diagnosed in a younger male patient. We discuss the findings of topographic maps, ultrasound pachymetry and the proposed treatment.Os autores relatam o caso de paciente jovem do sexo masculino que desenvolveu quadro de degeneração marginal pelúcida bilateral atípica, com afinamento corneal periférico de 360º, abordando ainda os aspectos dos mapas topográficos e os resultados obtidos com a paquimetria ultra-sônica, além do tratamento adotado.Hospital Oftalmológico de SorocabaHospital Oftalmológico de Sorocaba Setor de CórneaHospital Oftalmológico de Sorocaba Setor de Córnea e Doenças ExternasPontifícia Universidade Católica de SorocabaUNIFESP Departamento de OftalmologiaUNIFESP, Depto. de OftalmologiaSciEL