Differentials of the 2nd kind on a product surface

Abstract

This paper deals with the problems of representing an arbitrary double differential of the second kind, defined on a surface which is the topological product of two curves, in terms of the products of simple differentials of the second kind on the two curves. The curves are assumed to be non-singular and irreducible in a complex projective 2-space.

Keywords

• algebraic surface
• product surface
• algebraic curves
• double differential of the second kind
• simple differentials of the second kind
• Abelian differentials
• genus
• exterior product
• polar curves resultant.