# Algebraic boundaries among typical ranks for real binary forms

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Chiara Brambilla

created by angelini on 05 Mar 2018

16 mar 2018
-- 14:30

Aula Vitali, Dipartimento di Matematica, Università di Bologna

**Abstract.**

Binary real forms of degree d admit as typical ranks all the integers between $\lfloor d/2 \rfloor +1 $ and $d$. We investigate the boundary between the open subset of rank $r$ forms and the open subset of rank $r+1$.
These boundaries are known only in the extreme cases, by Lee-Sturmfels (between rank $\lfloor d/2 \rfloor +1 $ and $\lfloor d/2 \rfloor +2 $ and Comon-Ottaviani (between rank $ d-1 $ and $ d $). We investigate the intermediate boundaries.
In the talk I will present our new results, focusing on the case of degree 7 forms. This is work in progress with G.Stagliano'.