Betti numbers of Bresinsky’s curves in 𝔸4
Abstract
Bresinsky defined a class of monomial curves in 𝔸4 with the property that the minimal number of generators or the first Betti number of the defining ideal is unbounded above. We prove that the same behavior of unboundedness is true for all the Betti numbers and construct an explicit minimal free resolution for the defining ideal of this class of curves.
Communicated by T. H. Ha