WDVV EQUATIONS FROM ALGEBRA OF FORMS

A class of solutions to the WDVV equations is provided by period matri ces of hyperelliptic Riemann surfaces, with or without punctures. The equations themselves reflect associativity of explicitly described mul tiplicative algebra of (possibly meromorphic) one-differentials, which holds at least in the hyperelliptic case. This construction is direct generalization of the old one, involving the ring of polynomials fact orized over an ideal, and is inspired by the study of the Seiberg-Witt en theory. It has potential to be further extended to reveal algebraic structures underlying the theory of quantum cohomologies and the prep otentials in string models with N=2 supersymmetry.