Let Q = P-1 x P-1 and let C subset of 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 (HOQ)-O-1(r,-s) F -> (HOQ)-O-1( r + a,- s + b) 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 P-1 x P-1
Re, Riccardo
2012-01-01
Abstract
Let Q = P-1 x P-1 and let C subset of 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 (HOQ)-O-1(r,-s) F -> (HOQ)-O-1( r + a,- s + b) 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.
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