Ribbons are double structures on that arise as limits of canonical curves. They were first studied under this name in the 1990s by Bayer, Eisenbud, and Fong in connection with Green's Conjecture (now Voisin's Theorem). They also appear in Alper, Fedorchuk, and Smyth's recent proof of finite Hilbert stability for canonical curves. I will discuss some Groebner basis techniques that may be used to study degenerations of ribbons and discuss applications to computation of state polytopes.
