How does an algebraic geometer studying secant varieties further the understanding of
hypothesis tests in statistics? Why would a statistician working on factor analysis raise open …

We propose a new sufficient condition for verifying whether general rank-r complex tensors
of arbitrary order admit a unique decomposition as a linear combination of rank-1 tensors. A …

We consider here the problem, which is quite classical in Algebraic geometry, of studying
the secant varieties of a projective variety X. The case we concentrate on is when X is a …

We study syzygies of the Segre embedding of P (V 1)×⋯× P (V n), and prove two finiteness
results. First, for fixed p but varying n and V i, there is a finite list of master p-syzygies from …

We define a GL-variety to be an (typically infinite dimensional) algebraic variety equipped
with an action of the infinite general linear group under which the coordinate ring forms a …

We determine defining equations for the set of concise tensors of minimal border rank in C
m⊗ C m⊗ C m when m= 5 and the set of concise minimal border rank 1∗-generic tensors …

We introduce equivariant tree models in algebraic statistics, which unify and generalise
existing tree models such as the general Markov model, the strand symmetric model, and …

We determine normal forms and ranks of tensors of border rank at most three. We present a
differential-geometric analysis of limits of secant planes in a more general context. In …

Matrices of rank at most k are defined by the vanishing of polynomials of degree k+ 1 in their
entries (namely, their ((k+ 1)×(k+ 1))-subdeterminants), regardless of the size of the matrix …

arXiv:0809.1701v1 [math.AG] 10 Sep 2008 Page 1 arXiv:0809.1701v1 [math.AG] 10 Sep 2008
SECANT VARIETIES OF P1 ×···× P1 (n-TIMES) ARE NOT DEFECTIVE FOR n ≥ 5. MV …