CLASSIFICATION OF BETTI DIAGRAMS OF VARIETIES OF ALMOST MINIMAL DEGREE

Abstract

In this article we study the problem to determine all occurring Betti diagrams of varieties X subset of P(r) of almost minimal degree, i.e., deg(X) = codim(X, P(r)) + 2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim(X, P(r)) <= 8.