Related papers: Unexpected hypersurfaces of type $(d+k,d)$

This article describes a unirationality construction for general low degree complete intersections in projective space which is based on a variety of highly tangent lines. Applied to hypersurfaces, this implies that a general hypersurface…

Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…

In the recent articles by Alper, Eastwood and Isaev, it was conjectured that all rational $GL_n({\mathbb C})$-invariant functions of forms of degree $d\ge 3$ on ${\mathbb C}^n$ can be extracted, in a canonical way, from those of forms of…

Supersymmetry breaking and compactification of extra space-time dimensions may have a common dynamical origin if our universe is spontaneously generated in the form of a four-dimensional topological or non-topological defect in higher…

We study hypersurfaces either in the De Sitter space $\S_1^{n+1}\subset\R_1^{n+2}$ or in the anti De Sitter space $\H_1^{n+1}\subset\R_2^{n+2}$ whose position vector $\psi$ satisfies the condition $L_k\psi=A\psi+b$, where $L_k$ is the…

A bulge surface, on a time reflection-symmetric Cauchy slice of a holographic spacetime, is a non-minimal extremal surface that occurs between two locally minimal surfaces homologous to a given boundary region. According to the python's…

Let W be a projective variety of dimension n+1, L a free line bundle on W, X in $H^0(L^d)$ a hypersurface of degree d which is generic among those given by sums of monomials from $L$, and let $f : Y \to X$ be a generically finite map from a…

Several uniqueness results on compact maximal hypersurfaces in a wide class of sta- bly causal spacetimes are given. They are obtained from the study of a distinguished function on the maximal hypersurface, under suitable natural first…

A detailed study is made of super elliptic curves, namely super Riemann surfaces of genus one considered as algebraic varieties, particularly their relation with their Picard groups. This is the simplest setting in which to study the…

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…

We find the first examples of real hypersurfaces with two nonconstant principal curvatures in complex projective and hyperbolic planes, and we classify them. It turns out that each such hypersurface is foliated by equidistant Lagrangian…

We consider the locus of $r$-tuples of homogeneous forms of some fixed degree whose common vanishing locus in $\mathbb{P}^r$ is positive dimensional. We show that any component of maximal dimension of that locus either consists of…

We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining an even dimensional nodal hypersurface. This implies the validity of formulas due to M. Saito, L. Wotzlaw and…

We define the higher-order Alexander modules $A_{n,i}(\mathcal{U})$ and higher-order degrees $\delta_{n,i}(\mathcal{U})$ which are invariants of a complex hypersurface complement $\mathcal{U}$. These invariants come from the module…

We study irreducible subvarieties of the universal hypersurface $\mathcal{X}/B$ of degree $d$ and dimension $n$. We prove that when $d$ is sufficiently large, a degree $kd$ subvariety $Z$ which dominates $B$ comes from intersection with a…

In systems displaying a bulk first-order transition the order parameter may vanish continuously at a free surface, a phenomenon which is called surface-induced disorder. In the presence of surface-induced disorder the correlation lengths,…

We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model…

Let X be an irreducible hypersurface in $\mathbb{P}^n$ of degree $d\geq 3$ with only isolated semi-weighted homogeneous singularities, such that $exp(\frac{2\pi i}{k})$ is a zero of the Alexander polynomial. Then we show that the…

Lower-dimensional (hyper)surfaces that can carry gauge or gauge/gravitational anomalies occur in many areas of physics: one-plus-one-dimensional boundaries or two-dimensional defect surfaces in condensed matter systems, four-dimensional…

We give sharp lower bounds for the degree of the syzygies involving the partial derivatives of a homogeneous polynomial defining a nodal hypersurface. The result gives information on the position of the singularities of a nodal hypersurface…