The strongly robust simplicial complex of monomial curves

To every simple toric ideal IT I T one can associate the strongly robust simplicial complex Δ T Δ T , which determines the strongly robust property for all ideals that have IT I T as their bouquet ideal. We show that for the simple toric ideals of monomial curves in Aˢ A s , the strongly robust simplicial complex Δ T Δ T is either \∅ \ { ∅ } or contains exactly one 0-dimensional face. In the case of monomial curves in A³ A 3 , the strongly robust simplicial complex Δ T Δ T contains one 0-dimensional face if and only if the toric ideal IT I T is a complete intersection ideal with exactly two Betti degrees. Finally, we provide a construction to produce infinitely many strongly robust ideals with bouquet ideal the ideal of a monomial curve and show that they are all produced this way.