On the orlik-solomon algebra of a hypersolvable arrangement

Abstract EN

This paper is devoted to construct the Orlik-Solomon algebra of a hypersolvable r -arrangement by using the hypersolvable partition analogue.

We used the hypersolvable ordering which preserves the hypersolvable structure to define the NBC-basis of the Orlik-Solomon algebra and we embedded it in the partition module as a free graded submodule.

We used this ordering also to prove that a hypersolvable arrangement is quadratic if, and only if, it's fiber-type.

As a generalization of a result of Jambu and Papadima, we gave the quadratic Orlik-Solomon algebra a structure isomorphic to a partition module and we used this isomorphism to produce a comparison between the Orlik-Solomon algebra and the quadratic Orlik- Solomon algebra as free modules with many applications