On varieties of almost minimal degree in small codimension

The present research grew out of the authors' joint work [M. Brodmann, P. Schenzel, Arithmetic properties of projective varieties of almost minimal degree, J. Algebraic Geom., in press]. It continues the study of the structure of projective varieties of almost minimal degree, focusing to the case of small codimension. In particular, we give a complete list of all occurring Betti diagrams in the cases where codimX⩽4.