ON VANISHING THEOREMS FOR LOCAL SYSTEMS ASSOCIATED TO LAURENT POLYNOMIALS

Abstract

We prove some vanishing theorems for the cohomology groups of local systems associated to Laurent polynomials. In particular, we extend one of the results of Gelfand et al.[Generalized Euler integrals and$A$-hypergeometric functions, Adv. Math.84(1990), 255–271] to various directions. In the course of the proof, some properties of vanishing cycles of perverse sheaves and twisted Morse theory are used.