Let Q = ℙ 1 × ℙ 1 and let C = ⊆ Q be a curve of type (a, b) having equation F = 0. The main purpose of this paper is to analize the multiplicative structure of the bi-graded module H 1 *O Q, in particular to prove that for any r, s ≥ 0 the multiplication map induced by F has maximal rank for the general C of type (a, b). Interpretations of this problem in the contexts of multilinear algebra and differential algebra are emphasized.
Multiplications of maximal rank in the cohomology of P1×P1
RE, Riccardo
2012-01-01
Abstract
Let Q = ℙ 1 × ℙ 1 and let C = ⊆ Q be a curve of type (a, b) having equation F = 0. The main purpose of this paper is to analize the multiplicative structure of the bi-graded module H 1 *O Q, in particular to prove that for any r, s ≥ 0 the multiplication map induced by F has maximal rank for the general C of type (a, b). Interpretations of this problem in the contexts of multilinear algebra and differential algebra are emphasized.File in questo prodotto:
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