We use orbifold structures to deduce degeneracy statements for holomorphic maps into logarithmic surfaces. We improve former results in the smooth case and generalize them to singular pairs. In particular, we give applications on nodal surfaces and complements of singular plane curves.
2000 Mathematics Subject Classification: 68T01, 62H30, 32C09.Locally Linear Embedding (LLE) has gained prominence as a tool in unsupervised non-linear dimensional reduction. While the algorithm aims to preserve certain proximity relations between the observed points, this may not always be desirable if the shape in higher dimensions that we are trying to capture is observed with noise. This note suggests that a desirable first step is to remove or at least reduce the noise in the observations before...
It is shown that a sub-analytic set has a density at each point, and the notion of pure cone is defined. As in the complex case, this density may be expressed in terms of the area of the connected components of the pure tangent cone, with involved integral multiplicities.
On donne une condition suffisante explicite et générique pour qu’une forme de Pfaff à deux variables complexes ait ses feuilles denses tant localement que globalement.
We present a tameness property of sets definable in o-minimal structures by showing that Morse functions on a definable closed set form a dense and open subset in the space of definable functions endowed with the Whitney topology.