Memoirs of the American Mathematical Society 2002; 108 pp; softcover Volume: 158 ISBN10: 0821829270 ISBN13: 9780821829271 List Price: US$60 Individual Members: US$36 Institutional Members: US$48 Order Code: MEMO/158/753
 In this work, we prove a desingularization theorem for analytic families of twodimensional vector fields, under the hypothesis that all its singularities have a nonvanishing first jet. Application to problems of Singular Perturbations and Finite Cyclicity are discussed in the last chapter. Readership Graduate students and research mathematicians interested in several complex variables and analytic spaces. Table of Contents  Introduction
 Background material
 Nilpotent families and trivialization
 Desingularization of Nilpotent singularities
 The proof of the desingularization theorem
 Applications
 Bibliography
