Symmetry properties of tensors play an important role in physics. They correspond to the irreducible representations of the symmetric group, which can be described by young tableaux T. The global T-symmetrical tensor differential forms on the projective manifold Y define a birational invariant of Y. In the case of prime characteristic char(K)= p > 0 the pullback of the Frobenius provides an apportunity to define further discrete birational invariants of algebraic manifolds using the ps-th powers (df)p¨' instead of the differentials df. Using Sernesis result on infinitesimal deformations an explicit formula for the moduli space dimension of complete intersections is given. As an application among others a conjecture of Libgober and Wood will be confirmed concerning the existence of diffeomorphic three-dimensional complete interactions which lie in different dimensional components of the moduli space. Finally for arbitrary locally free sheaves F o Y the Chern classes of the T-power FT are calculated as polynomials in Chern classes of F.