Let X ⊆ PN be a non-degenerate projective variety of dimension d. Then the sth secant variety of X, denoted σs(X), is the Zariski closure of the union of linear spans of s-tuples of points lying on X. The study of secant varieties has a long history. The interest in this subject goes back to the Italian school at the turn of the 20th century. This topic has received renewed interest over the pa...

Motivated by results on the rationality of equivariant Hilbert series some hierarchical models in algebraic statistics we introduce Segre product formal languages and apply it to establish new cases. To this end show that two regular is again regular. We also prove every filtration algebras given as a tensor families with rational has series. The term used broadly include action monoid nonnegat...

In this paper, we consider local holomorphic mappings f : M → M ′ between real algebraic CR generic manifolds (or more generally, real algebraic sets with singularities) in the complex euclidean spaces of different dimensions and we search necessary and sufficient conditions for f to be algebraic. These conditions appear to exclude two certain flatness of M and of M ′. From the point of view of...

Let V be a closed subscheme of a projective space P. We give an algorithm to compute the Chern-Schwartz-MacPherson class, and the Euler characteristic of V and an algorithm to compute the Segre class of V . The algorithms can be implemented using either symbolic or numerical methods. The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a h...

The CANDECOMP/PARAFAC (CP) tensor decomposition is a crucial data analysis and processing technique in applications and sciences. Tensors admitting a CP decomposition of rank at most s can be considered points of the sth order secant variety of a Segre variety, yet the most basic invariant of this variety—its dimension— is not yet fully understood. A conjecture was nevertheless proposed in [H. ...

We study syzygies of the Segre embedding of P(V1) × · · · × P(Vn), and prove two finiteness results. First, for fixed p but varying n and Vi, there is a finite list of “master p-syzygies” from which all other p-syzygies can be derived by simple substitutions. Second, we define a power series fp with coefficients in something like the Schur algebra, which contains essentially all the information...

§0. Introduction §1. Preliminaries, notation, and definitions §2. Basic approaches and preliminary facts §3. Extension across M 1 §4. Extension across C t §5. Completion of the proof of the Main Theorem— Assuming Theorem C §6. Statement of Theorem D and related notation §7. Extension of G(f, λ)—Proof of Theorem D(a) §8. Branches of F and Segre varieties §9. Branch locus of F and Segre varieties...

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and dimension of the group orbits as well as the Petrov type are constant, the aim of this work is to include the Segre types of the Ricci tensor (and hence of the Eins...