The Tjurina ideal of a germ holomorphic function f is the

We study the expected behavior of Betti numbers arrangements zeros random (distributed according to Kostlan distribution) polynomials in R P n $\mathbb {R}\mathrm{P}^n$ . Using a spectral sequence, we prove an asymptotically exact estimate on number connected components complement s $s$ such hypersurfaces also investigate same problem case where are defined by quadratic polynomials. In this cas...

In this article, we consider hypersurfaces moving with normal velocity depending on the timespace coordinates and on the normal to the hypersurface. We naturally define a measure associated to this hypersurface. This measure is defined on a suitable space/unit normal/curvature configuration space. We show that, while the hypersurface stays smooth, then the measure is a solution to a linear tran...

Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...