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http://dx.doi.org/10.4134/JKMS.2011.48.5.1001

CLASSIFICATION OF BETTI DIAGRAMS OF VARIETIES OF ALMOST MINIMAL DEGREE  

Lee, Wan-Seok (Department of Mathematical Sciences Korea Advanced Institute of Science and Technology)
Park, Eui-Sung (Department of Mathematics Korea University)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.5, 2011 , pp. 1001-1015 More about this Journal
Abstract
In this article we study the problem to determine all occurring Betti diagrams of varieties $X{\subset}\mathbb{P}^r$ of almost minimal degree, i.e. deg(X) = codim(X; $\mathbb{P}^r$)+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$(X,\mathbb{P}^r){\leq}8$.
Keywords
minimal free resolution; Betti number; rational normal scroll; varieties of low degree;
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