Related papers: Enumeration of singular hypersurfaces on arbitrary…
An automorphism on a complex supermanifold $\mathcal M$ is called unipotent if it reduces to the identity on the associated graded supermanifold $gr(\mathcal M)$. These automorphisms are close to be complementary to those responsible for…
In this paper we construct a Universal chain complex, counting zeros of closed 1-forms on a manifold. The Universal complex is a refinement of the well known Novikov complex; it relates the homotopy type of the manifold, after a suitable…
The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct…
We describe singularities of the convex hull of a generic compact smooth hypersurface in four-dimensional affine space up to diffeomorphisms. It turns out there are only two new singularities (in comparison with the previous dimension case)…
We compute the topological simple structure set of closed manifolds which occur as total spaces of flat bundles over lens spaces S^l/(Z/p) with fiber an n-dimensjional torus T^n for an odd prime p and l greater or equal to 3, provided that…
In this paper, we study hypersurfaces of Euclidean spaces with arbitrary dimension. First, we obtain some results on $\mbox{H}$-hypersurfaces. Then, we give the complete classification of $\mbox{H}$-hypersurfaces with 3 distinct curvatures.…
We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…
For a hypersurface in a projective space, we consider the set of pairs of a point and a line in the projective space such that the line intersects the hypersurface at the point with a fixed multiplicity. We prove that this set of pairs…
We extend the Hirzebruch-Milnor class of a hypersurface $X$ to the case where the normal bundle is nontrivial and $X$ cannot be defined by a global function, using the associated line bundle and the graded quotients of the monodromy…
We investigate a necessary condition for a compact complex manifold X of dimension n in order that its universal cover be the Cartesian product $C^n$ of a curve $C = \PP^1 or \HH$: the existence of a semispecial tensor $\omega$. A…
In this paper we give the first example of a surface bundle over a surface with at least three fiberings. In fact, for each $n \ge 3$ we construct $4$-manifolds $E$ admitting at least $n$ distinct fiberings $p_i: E \to \Sigma_{g_i}$ as a…
A unimodular complex surface is a complex 2-manifold X endowed with a holomorphic volume form. A strictly pseudoconvex real hypersurface M in X inherits not only a CR-structure but a canonical coframing as well. In this article, this…
We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected)…
We show that the Chern-Schwartz-MacPherson class of a hypersurface X in a nonsingular variety M `interpolates' between two other notions of characteristic classes for singular varieties, provided that the singular locus of X is smooth and…
Let $C$ be the rational normal curve of degree $e$ in $\mathbb{P}^n$, and let $X\subset \mathbb{P}^n$ be a degree $d\ge 2$ hypersurface containing $C$. In previous work, I. Coskun and E. Riedl showed that the normal bundle $N_{C/X}$ is…
A supersymmetric solution of 5d supergravity may admit an `evanescent ergosurface': a timelike hypersurface such that the canonical Killing vector field is timelike everywhere except on this hypersurface. The hyperk\"ahler `base space' of…
In this paper we compute upper bounds for the number of ordinary triple points on a hypersurface in $P^3$ and give a complete classification for degree six (degree four or less is trivial, and five is elementary). But the real purpose is to…
Let X be a (possibly nodal) K-trivial threefold moving in a fixed ambient space P. Suppose X contains a continuous family of curves, all of whose members satisfy certain unobstructedness conditions in P. A formula is given for computing the…
We derive a formula for the Milnor class of scheme-theoretic global complete intersections (with arbitrary singularities) in a smooth variety in terms of the Segre class of its singular scheme. In codimension one the formula recovers a…
We classify all real hypersurfaces with three distinct constant principal curvatures in complex hyperbolic spaces of dimension greater than two.