On the rank of a partially symmetric tensor

Every partially symmetric tensor can be expressed as a linear combination of a finite number of so-called decomposable partially symmetric tensors. The rank of a partially symmetric tensor is defined as the smallest positive integer r such that the partially symmetric tensor can be written as a linear combination of r decomposable partially symmetric tensors. In this talk, we discuss an algebro-geometric approach to the problem of finding the generic rank of partially symmetric tensors, that is, the rank of a generic partially symmetric tensor.