A -web is given by complex analytic foliations of codimension in such that the leaves are in general position. We are interested in the geometry of such configurations. A complex of -vector spaces is defined in which corresponds to functions and to -forms of the web for . If with , it is proved that is a finite analytic invariant of with an optimal upper bound for . These bounds generalize the Castelnuovos ones for genus of curves in with degree . Some characterization of the the space of abelian differentials to an algebraic variety in of pure dimension with degree is given. Moreover, using duality and Abels theorem, we investigate how for suitable the natural complex and the abelian relation complex of the linear web associated to in are related.
Cite this article
Alain Hénaut, Formes différentielles abéliennes, bornes de Castelnuovo et géométrie des tissus. Comment. Math. Helv. 79 (2004), no. 1, pp. 25–57DOI 10.1007/S00014-003-0787-4