Related papers: Degree of the 3-secant variety

Every $\mathbb{A}^{1}-$bundle over the complex affine plane punctured at the origin, is trivial in the differentiable category but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of…

Two well studied invariants of a complex projective variety are the unit Euclidean distance degree and the generic Euclidean distance degree. These numbers give a measure of the algebraic complexity for "nearest" point problems of the…

The goal of this paper is to start a study of aCM and Ulrich sheaves on non-integral projective varieties. We show that any aCM vector bundle of rank two on the double plane is a direct sum of line bundles. As a by-product, any aCM vector…

If $\X \subset \P^n$ is a reduced and irreducible projective variety, it is interesting to find the equations describing the (higher) secant varieties of $\X$. In this paper we find those equations in the following cases: $\X =…

We find all possible isomorphisms and 3-birational maps (i.e., birational maps which induce an isomorphism between open subsets whose respective complements have codimension at least 3) between moduli spaces of parabolic vector bundles with…

We study the representations of a class of non-commutative polynomial algebras truncated at degree 3, with one additional relation. We determine the irreducible components of their varieties of representations. We do this by showing that…

We study the dimensions of secant varieties of the Grassmannian of Lagrangian subspaces in a symplectic vector space. We calculate these dimensions for third and fourth secant varieties. Our result is obtained by providing a normal form for…

We study deformation of tube algebra under twisting of graded monoidal categories. When a tensor category $\mathcal{C}$ is graded over a group $\Gamma$, a torus-valued 3-cocycle on $\Gamma$ can be used to deform the associator of…

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional…

The notion of higher order dual varieties of a projective variety is a natural generalization of the classical notion of projective duality, introduced by Piene in 1983. In this paper we study higher order dual varieties of projective toric…

Given the space $V={\mathbb P}^{\binom{d+n-1}{n-1}-1}$ of forms of degree $d$ in $n$ variables, and given an integer $\ell>1$ and a partition $\lambda$ of $d=d_1+\cdots+d_r$, it is in general an open problem to obtain the dimensions of the…

We obtain a recursive formula for the characteristic number of degree $d$ curves in $\mathbb{P}^2$ with prescribed singularities (of type $A_k$) that are tangent to a given line. The formula is in terms of the characteristic number of…

The Milnor degree of a 3-manifold is an invariant that records the maximum simplicity, in terms of higher order linking, of any link in the 3-sphere that can be surgered to give the manifold. This invariant is investigated in the context of…

We establish a criterion for a complex number to be algebraic over Q of degree at most two. It requires that, for any sufficiently large real number X, there exists a non-zero polynomial with integral coefficients, of degree at most two and…

Let $G$ be a simple graph and $v$ be a vertex of $G$. The triangle-degree of $v$ in $G$ is the number of triangles that contain $v$. While every graph has at least two vertices with the same degree, there are graphs in which every vertex…

We describe a classification of degree n complex coefficient polynomials with respect to combinatorial patterns that arise from the two real algebraic curves obtained as the zero sets for their real and imaginary part. In particular, we…

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one, X, comes from the…

Resolvent degree is an invariant measuring the complexity of algebraic and geometric phenomena, including the complexity of finite groups. To date, the resolvent degree of a finite simple group $G$ has only been investigated when $G$ is a…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

We study the dimension of the higher secant varieties $X^s$ of ${\Bbb X} = {\Bbb P}^{n_1}\times ...\times {\Bbb P}^{n_t}$ embedded the morphism given by ${\cal O}_{\Bbb X}({a_1,...,a_t})$. We call it a {\it Segre-Veronese variety} and the…