SUMMARY Reflector-normal angles and reflector-curvature parameters are the principal geometric attributes used in seismic interpretation for characterizing orientations shapes, respectively, of geological reflecting surfaces. Commonly, input data set their computation consists fine 3-D grids scalar fields representing either seismic-driven reflectivities (e.g. amplitudes migrated volumes) or mo...

Abstract We investigate the arrangement of hypersurfaces on a nonsingular varieties whose associated logarithmic vector bundle is arithmetically Cohen–Macaulay (for short, aCM), and prove that projective space only smooth complete intersection with Picard rank one admits an aCM bundle. also obtain number results bundles over several specific varieties. As opposite situation we Torelli‐type prob...

We prove that the polar degree of an arbitrarily singular projective hypersurface can be decomposed as a sum non-negative numbers which represent local vanishing cycles two different types. This yields lower bounds for any hypersurface.

We prove that for any germ of complex analytic set in Cn there exists a hypersurface singularity whose Milnor fibration has trivial geometric monodromy and fibre homotopic to the complement of the germ of complex analytic set. As an application we show an example of a quasi-homogeneous hypersurface singularity, with trivial geometric monodromy and simply connected and non-formal Milnor fibre.

This paper shows that the general hypersurface of degree ≥ 6 in projective four space cannot support an indecomposable rank two vector bundle which is Arithmetically CohenMacaulay and four generated. Equivalently, the equation of the hypersurface is not the Pfaffian of a four by four minimal skewsymmetric matrix.

In this paper we prove the birational superrigidity and nonrationality of a hypersurface X ⊂ P of degree 6 such that the hypersurface X does not contain three-dimensional linear subspaces of P and the only singularities of X are isolated ordinary double points.

We prove the non-rationality of a double cover of P branched over a hypersurface F ⊂ P of degree 2n having isolated singularities such that n ≥ 4 and every singular points of the hypersurface F is ordinary, i.e. the projectivization of its tangent cone is smooth, whose multiplicity does not exceed 2(n− 2).

Constructions of metrics with special holonomy by methods of exterior differential systems are reviewed and the interpretations of these construction as ‘flows’ on hypersurface geometries are considered. It is shown that these hypersurface ‘flows’ are not generally well-posed for smooth initial data and counterexamples to existence are constructed.