Let H be a polynomial of degree m+. 1 on C2 such that its generic fiber is biholomorphic to C*, and let ω be an arbitrary polynomial 1-form of degree n on C2. 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 ω. © 2012 Elsevier Ltd.
- Abelian integrals
- Weak Hilbert's 16th problem