Abstract

Let H be a polynomial of degree m + 1 on C-2 such that its generic fiber is biholomorphic to C*, and let omega be an arbitrary polynomial 1-form of degree n on C-2. We give an upper bound depending only on m and n for the number of isolated zeros of the complete Abelian integral defined by H and omega. (C) 2012 Elsevier Inc. All rights reserved.