Pencils of singular quadrics of constant rank and their orbits

Abstract

We give a geometric description of singular pencils of quadrics of constant rank, relating them to the splitting type of some naturally associated vector bundles on ${\mathbb{P}}^1$. Then we study their orbits in the Grassmannian of lines, under the natural action of the general linear group.

arXiv commentDedicated to Giorgio Ottaviani on the occasion of his 60th birthday. 17 pages, 2 figures