Throughout this note all rings are commutative, and A is a fixed ring. If S, T are graded A-algebras then the tensor product S ⊗A T becomes a graded A-algebra in a canonical way with the grading given by (TES,Lemma 13). That is, S ⊗A T is the coproduct of the morphisms of A-modules Sd ⊗A Te −→ S ⊗A T for d, e ≥ 0. The canonical morphisms p1 : S −→ S ⊗A T, p2 : T −→ S ⊗A T are then morphisms of ...

We define flocks of Segre varieties Sn; n as a generalization of flocks of Q þð3; qÞ, studying the connections with translation planes.

We classify the tangential varieties of Segre–Veronese which are Cohen–Macaulay or Gorenstein.

A characterization of certain elliptic quadrics Q−(3, q) embedded in the Hermitian surface of PG(3, q2), q odd, as special sets (after Shult [4]) in terms of Segre invariants, is given.

We define many new examples of modules of equations for secant varieties of Segre varieties that generalize Strassen’s commutation equations [7]. Our modules of equations are obtained by constructing subspaces of matrices from tensors that satisfy various commutation properties.

This paper deals with syzygies of the ideals of the Segre embeddings. Let d ≥ 3 and n1, ..., nd ∈ N − {0}. We prove that OPn1×....×Pnd (1, ..., 1) satisfies Green-Lazarsfeld’s Property Np if and only if p ≤ 3.

In this paper we discuss the notion of singular vector tuples of a complex valued d-mode tensor of dimension m1 × . . . × md. We show that a generic tensor has a finite number of singular vector tuples, viewed as points in the corresponding Segre product. We give the formula for the number of singular vector tuples. We show similar results for tensors with partial symmetry. We give analogous re...

A point $p$ in a projective space is $h$-identifiable via variety $X$ if there unique way to write as linear combination of $h$ points $X$. Identifiability important both algebraic geometry and applications. In this paper we propose an entirely new approach study identifiability, connecting it the notion secant defect for any smooth variety. are able improve known bounds on identifiability prod...