Title: A polynomial bound on the regularity of an ideal in terms of half of the syzygies
Abstract:Let K be a field and let S = K[x 1 , . . ., x n ] be a polynomial ring.Consider a homogenous ideal I ⊂ S. Let t i denote reg(Tor S i (S/I, K)), the maximal degree of an ith syzygy of S/I.We prove boun...Let K be a field and let S = K[x 1 , . . ., x n ] be a polynomial ring.Consider a homogenous ideal I ⊂ S. Let t i denote reg(Tor S i (S/I, K)), the maximal degree of an ith syzygy of S/I.We prove bounds on the numbers t i for i > n 2 purely in terms of the previous t i .As a result, we give bounds on the regularity of S/I in terms of as few as half of the numbers t i .We also prove related bounds for arbitrary modules.These bounds are often much smaller than the known doubly exponential bound on regularity purely in terms of t 1 .Read More