A Note on the Differential Forms on Everywhere Normal Varieties

Extract

A. Weil proposed in his book “Foundations of algebraic geometry” several problems concerning differential forms on algebraic varieties, S. Koizumi has proved that if ω is a differential form on a complete variety U without multiple point, which is finite at every point of IT, then ω is the differential form of the first kind. The following example shows that on everywhere normal varieties with multiple points this statement holds no more; that is: A differential form on a everywhere normal variety which is finite on every simple point of its variety is not always the differential form of the first kind.