Related papers: Vector field construction of Segre sets

This paper explores the dimensions of higher secant varieties to Segre-Veronese varieties. The main goal of this paper is to introduce two different inductive techniques. These techniques enable one to reduce the computation of the…

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen's commutation equations. Our modules of equations are obtained by constructing subspaces of matrices from tensors that…

Let V be a real hypersurface of class C^k, k>=3, in a complex manifold M of complex dimension n+1, HT(V) the holomorphic tangent bundle to V giving the induced CR structure on V. Let \theta be a contact form for (V,HT(V)), \xi_0 the Reeb…

We determine the minimal generators of the ideal of the tangential variety of a Segre-Veronese variety, as well as the decomposition into irreducible GL-representations of its homogeneous coordinate ring. In the special case of a Segre…

Let K=Fq be a finite field. We introduce a family of projective Reed-Muller-type codes called projective Segre codes. Using commutative algebra and linear algebra methods, we study their basic parameters and show that they are direct…

We classify 1-dimensional connected dually flat manifolds $M$ that are toric in the sense of [Molitor, arXiv:2109.04839], and show that the corresponding torifications are complex space forms. Special emphasis is put on the case where M is…

We show that under mild assumptions the Segre product of two graded cluster algebras has a natural cluster algebra structure.

The rational homology groups of the packing complexes are important in algebraic geometry since they control the syzygies of line bundles on projective embeddings of products of projective spaces (Segre--Veronese varieties). These complexes…

We introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form classification of these vector fields. We show that the…

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.

A singular foliation $\mathcal F$ gives a partition of a manifold $M$ into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space $M / \mathcal…

Let $\mathcal{F}$ be a foliation defined on a complex projective manifold $M$ of dimension $n$ and admitting a holomorphic vector field $X$ tangent to it along some non-empty Zariski-open set. In this paper we prove that if $X$ has…

The paper studies the generic complex 1-dimensional polynomial vector fields of the form $iP(z)\frac{\partial}{\partial z}$, where $P$ is a polynomial with real coefficients, under topological orbital equivalence preserving the separatrices…

For a closed symplectic manifold $(M,\omega)$, a compatible almost complex structure $J$, a 1-periodic time dependent symplectic vector field $Z$ and a homotopy class of closed curves $\gamma$ we define a Floer complex based on 1-periodic…

We establish basic techniques for studying the ideals of secant varieties of Segre varieties. We solve a conjecture of Garcia, Stillman and Sturmfels on the generators of the ideal of the first secant variety in the case of three factors…

A quadratic line complex is a three-parameter family of lines in projective space P^3 specified by a single quadratic relation in the Plucker coordinates. Fixing a point p in P^3 and taking all lines of the complex passing through p we…

In this paper we give a geometric description of the foliation of a generic real analytic family unfolding a real analytic vector field with a weak focus at the origin, and show that two such families are orbitally analytically equivalent…

In this paper we study the action of complex conjugation on Shimura varieties and the problem of descending these to the maximal totally real field of the reflex field. We prove the existence of such descent for many Shimura varieties whose…

A rigorous mathematical proof is given of a class of vector identities that provide a way to separate an arbitrary vector field (over a linear space) into the sum of a radial (i.e., pointing toward the radial unit vector) vector field,…

It is shown that a germ of a holomorphic mapping sending a real-analytic generic submanifold of finite type into another is determined by its projection on the Segre variety of the target manifold. A necessary and sufficient condition is…