Resumen de Linear syzygies, flag complexes, and regularity

Alexandru Constantinescu, Thomas Kahle, Matteo Varbaro

• We show that for every ?∈ℤ>0 there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to ? . For Gorenstein ideals we prove that the regularity of their quotients can not exceed four, thus showing that for ?>4 every triangulation of a ? -manifold has a hollow square or simplex. We also show that for most monomial ideals generated in degree two and with linear syzygies the regularity is ?(log(log(?)) , where ? is the number of variables.