Gleb Nenashev: A generalized super fermat problem for binary forms

Abstract: The space Pol_d ≃ CP^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 with the multiplicities of their distinct roots given by a fixed partition μ ⊢ d. For each such stratum S_μ, we introduce its secant degeneracy index lμ which is the minimal number of projectively dependent pairwise distinct points on S_μ, i.e., points whose projective span has dimension smaller than l_μ − 1. We obtain several results about lμ and apply them to the super Fermat problem for binary forms.