Related papers: Determinantal representations of singular hypersur…

Let $X$ be a projective variety (possibly singular) over an algebraically closed field of any characteristic and $\mathcal{F}$ be a coherent sheaf. In this article, we define the determinant of $\mathcal{F}$ such that it agrees with the…

We investigate the global variation of moduli of linear sections of a general hypersurface. We prove a "generic Torelli" result for a large proportion of cases, and we obtain a complete picture of the global variation of moduli of line…

Given an algebraic variety $X\subset\mathbb{P}^N$ with stabilizer $H$, the quotient $PGL_{N+1}/H$ can be interpreted a parameter space for all $PGL_{N+1}$-translates of $X$. We define $X$ to be a $\textit{homogeneous variety}$ if $H$ acts…

We prove the existence of rotational hypersurfaces in $\mathbb{H}^n\times \mathbb{R}$ with $H_{r+1}=0$ and we classify them. Then we prove some uniqueness theorems for $r$-minimal hypersurfaces with a given (finite or asymptotic) boundary.…

We prove that convex-cocompact representations of finitely generated groups in the group of isometries of the infinite-dimensional hyperbolic space form an open set in the space of representations, allowing us to deform these…

Significant research has been carried out in the past half-century on defining generalised determinants for transformations between (typically real) vector spaces of different dimensions. We review three different generalisations of the…

We study tridimensional tensors on the complex field from the point of view of hypermatrices, taking into consideration the problem of determining whether they are degenerate or not, concise or not, what is their essential format if they…

We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…

A form in a polynomial ring over a field is said to be homaloidal if its polar map is a Cremona map, i.e., if the rational map defined by the partial derivatives of the form has an inverse rational map. The object of this work is the search…

We find a spinorial representation of a Riemannian or Lorentzian surface in a Lorentzian homogeneous space of dimension $3.$ We in particular obtain a representation theorem for surfaces in the $\mathbb{L}(\kappa,\tau)$ spaces. We then…

We give a short combinatorial proof of the generic invertibility of the Hasse-Witt matrix of a projective hypersurface. We also examine the relationship between the Hasse-Witt matrix and certain $A$-hypergeometric series, which is what…

An arbitrary Mueller matrix can be decomposed into a sum of up to four deterministic Mueller-Jones matrices, with strengths given by the eigenvalues of an associated Hermitian matrix. A geometrical representation of the eigenvalues in terms…

We study the modular representation theory of the symmetric and alternating groups. One of the most natural ways to label the irreducible representations of a given group or algebra in the modular case is to show the unitriangularity of the…

Under the natural action of the pure mapping class group of a surface of genus at least three, we show that any global fixed point in the low-dimensional deformation space of the surface group corresponds to the trivial representation. A…

For a subvariety of a smooth projective variety, consider the family of smooth hypersurfaces of sufficiently large degree containing it, and take the quotient of the middle cohomology of the hypersurfaces by the cohomology of the ambient…

A monoid hypersurface is an irreducible hypersurface of degree d which has a singular point of multiplicity d-1. Any monoid hypersurface admits a rational parameterization, hence is of potential interest in computer aided geometric design.…

We give a brief report on our computations of linear determinantal representations of smooth plane cubics over finite fields. After recalling a classical interpretation of linear determinantal representations as rational points on the…

This is the second of a pair of papers on extended geometrically finite (EGF) representations, which were originally posted as a single article under the title "An extended definition of Anosov representation for relatively hyperbolic…

We characterize embedded $\C^1$ hypersurfaces of $\R^n$ as the only locally closed sets with continuously varying flat tangent cones whose measure-theoretic-multiplicity is at most $m<3/2$. It follows then that any (topological)…

Isolated hypersurface singularities come equipped with distinguished bases of their Milnor lattices and with upper triangular integral matrices, which are called here distinguished matrices. These matrices form an orbit of a braid group and…