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arXiv · 1006.5124

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

Salvatore Giuffrida·Renato Maggioni·Riccardo Re
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Abstract

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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Salvatore Giuffrida, Renato Maggioni, Riccardo Re. 2010-06-26. Multiplications of Maximal Rank in the Cohomology of P^1\times P ^1. https://arxiv.org/abs/1006.5124

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