We study the interplay between the properties of the germ of a singular variety N ⊂ Rn given in the title and the algebra of vector fields tangent to N . The Poincare lemma property means that any closed differential (p+1)-form vanishing at any point ofN is a differential of a p-form which also vanishes at any point of N . In particular, we show that the classical quasi-homogeneity is not a nec...

We show that Ambro–Kawamata’s non-vanishing conjecture holds true for a quasi-smooth WCI X which is Fano or Calabi-Yau, i.e. we prove that, if H is an ample Cartier divisor on X , then |H | is not empty. If X is smooth, we further show that the general element of |H | is smooth. We then verify Ambro–Kawamata’s conjecture for any quasi-smooth weighted hypersurface. We also verify Fujita’s freene...

This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compacti...

Smooth K-functors are introduced and the smooth K-theory of locally convex algebras is developed. It is proved that the algebraic and smooth K-functors are isomorphic on the category of quasi ⊗̂-stable real (or complex) Fréchet algebras.

The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by ...

— We establish the correspondence between tame harmonic bundles and μL-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for μL-stable parabolic Higgs bundles. Then we show that any local system on a smooth quasi projective variety can be deformed to a variation of polarized Hodge structure. As a consequence, we can conclude ...

Scanning tunneling microscopy and spectroscopy are employed in order to map with nanometer resolution the local quasi-particle density of states in superconducting proximity structures. Our experimental configuration is unique, in that the tunneling current flows in parallel to the interfaces between different materials. We focus here on the measurement of bound and resonant states, arising fro...

We study the ideals of the rational cohomology ring of the Hilbert scheme X [n] of n points on a smooth projective surface X . As an application, for a large class of smooth quasi-projective surfaces X , we show that every cup product structure constant of H∗(X ) is independent of n; moreover, we obtain two sets of ring generators for the cohomology ring H∗(X ). Similar results are established ...