arXiv subjects

S. Janeczko

Publications and source records attributed to S. Janeczko.

3 recordsLinked to original sources

arXiv2015

Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space

For a generic embedding of a smooth closed surface $M$ into $\mathbb R^4$, the subset of $\mathbb R^4$ which is the affine $λ$-equidistant of $M$ appears as the discriminant set of a stable mapping $M \times M \to \mathbb R^4$, hence their stable singularities are $A_k, \, k=2, 3, 4,$ and $C_{2,2}^{\pm}$. In this paper, we characterize these stable singularities of $λ$-equidistants in terms of the bi-local extrinsic geometry of the surface, leading to a geometrical study of the set of weakly parallel points on $M$.

math.DG↗

arXiv2014

On a generic symmetry defect hypersurface

Let f : X -> Y be a dominant polynomial mapping of affine varieties. For generic y in Y we have Sing(f^{-1}(y)) = f^{-1}(y) \cap Sing(X): As an application we show that symmetry defect hypersurfaces for two generic members of the irreducible algebraic family of n-dimensional smooth irreducible subvarieties in general position in C^{2n} are homeomorphic and they have homeomorphic sets of singular points. In particular symmetry defect curves for two generic curves in C^2 of the same degree have the same number of singular points.

math.AG↗

arXiv2012

Generic singularities of symplectic and quasi-symplectic immersions

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

math.SG↗