Multiplications of Maximal Rank in the Cohomology of P^1\times P ^1

Details Multiplications of Maximal Rank in the Cohomology of P^1\times P ^1 Multiplications of Maximal Rank in the Cohomology of P^1\times P ^1

2010-06-26

arxiv.org/abs/1006.5124v1

Mathematics

Algebraic Geometry

To appear in Collectanea Mathematica

Scientific paper

We show that the linear map defined by multiplication with a general bi-homogeneous form between two bi-graduated pieces of the first cohomology of a nonsingular quadric in the projective space is of maximal rank. This is the first non trivial case of a more general open problem on natural linear maps between vector spaces of tensors defined in terms of multiplications and contractions. An interpretation in terms of bi-homogeneous linear differential operators with polynomial coefficients is also given.

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