Abstract
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 codim X ⩽ 4 .
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