Partially umbilic singularities of hypersurfaces of R4

Umbilic and Tangential Singularities on Configurations of Principal Curvature Lines

In this paper is studied the relationship between quadratic tangencies of principal lines with the boundary of a surface and the Darbouxian umbilics of a smooth boundaryless surface which approximates it through the process of thickening and smoothing defined here.

Stringy E-functions of hypersurfaces and of Brieskorn singularities

We show that for a hypersurface Batyrev’s stringy E-function can be seen as a residue of the Hodge zeta function, a specialization of the motivic zeta function of Denef and Loeser. This is a nice application of inversion of adjunction. If an affine hypersurface is given by a polynomial that is non-degenerate with respect to its Newton polyhedron, then the motivic zeta function and thus the stri...

Milnor Numbers of Projective Hypersurfaces with Isolated Singularities

Let V be a projective hypersurface of fixed degree and dimension which has only isolated singular points. We show that, if the sum of the Milnor numbers at the singular points of V is large, then V cannot have a point of large multiplicity, unless V is a cone. As an application, we give an affirmative answer to a conjecture of Dimca and Papadima.

Flavour from partially resolved singularities

In this letter we study topological open string field theory on D–branes in a IIB background given by non compact CY geometries O(n) ⊕ O(−2 − n) on P with a singular point at which an extra fiber sits. We wrap N D5-branes on P1 and M effective D3-branes at singular points, which are actually D5–branes wrapped on a shrinking cycle. We calculate the holomorphic Chern-Simons partition function for...

The topology of isolated singularities on complex hypersurfaces