Resumen de Multiplications of maximal rank in the cohomology of ℙ1×ℙ1

Salvatore Giuffrida, Renato Maggioni, Riccardo Re

• Let ?=ℙ1×ℙ1 and let ?⊆? 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 ?1∗?? , in particular to prove that for any r, s ≥ 0 the multiplication map ?1??(?,−?)⟶??1??(?+?,−?+?) 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.