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.
@article{1622,
title = {Tensor Differential Forms and Some Birational Invariants of Projective Manifolds},
journal = {CUBO, A Mathematical Journal},
volume = {7},
year = {2005},
language = {en},
url = {http://dml.mathdoc.fr/item/1622}
}
Brückmann, P. Tensor Differential Forms and Some Birational Invariants of Projective Manifolds. CUBO, A Mathematical Journal, Tome 7 (2005) . http://gdmltest.u-ga.fr/item/1622/