Hilbert coefficients and sequentially Cohen-Macaulay modules
  The purpose of this paper is to present a characterization of sequentially Cohen-Macaulay modules in terms of its Hilbert coefficients with respect to distinguished parameter ideals. The formulas involve arithmetic degrees. Among corollaries of the main result we obtain a short proof of Vasconcelos Vanishing Conjecture for modules and an upper bound for the first Hilbert coefficient. 
Nguyen Tu Cuong, Shiro Goto and Hoang Le Truong
math.AC