Ideals generated by quadrics

Our purpose is to study the cohomological properties of the Rees algebras of a class of ideals generated by quadrics. For all such ideals I⊂R=K[x,y,z] we give the precise value of depthR[It] and decide whether the corresponding rational maps are birational. In the case of dimension d≥3, when K=R, we give structure theorems for all ideals of codimension d minimally generated by (d+12)−1 quadrics. For arbitrary fields K, we prove a polarized version.