Secant degeneracy index of the standard strata in the space of binary forms

Abstract

The space $Pol_d\simeq \bC P^d$ of all complex-valued binary forms of degree $d$ (considered up to a constant factor) has a standard stratification, each stratum of which contains all forms whose set of multiplicities of their distinct roots is given by a fixed partition $\mu ⊢d$. For each such stratum $S_{\mu },$ we introduce its secant degeneracy index ${\ell }_{\mu }$ which is the minimal number of projectively dependent pairwise distinct points on $S_{\mu }$, i.e., points whose projective span has dimension smaller than ${\ell }_{\mu }-1$. In what follows, we discuss the secant degeneracy index ${\ell }_{\mu }$ and the secant degeneracy index ${\ell }_{\bar{\mu }}$ of the closure ${\bar{S}}_{\mu }$.

11 pages

References in corpus (1)

• On generic identifiability of symmetric tensors of subgeneric rank

Cited by in corpus (1)

• Linearly dependent powers of binary quadratic forms