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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)
  • 투고 : 2010.05.22
  • 발행 : 2011.09.01

초록

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$(X,\mathbb{P}^r){\leq}8$.

키워드

참고문헌

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피인용 문헌

  1. Projective subvarieties having large Green–Lazarsfeld index vol.351, pp.1, 2012, https://doi.org/10.1016/j.jalgebra.2011.10.041
  2. On syzygies of divisors on rational normal scrolls vol.287, pp.11-12, 2014, https://doi.org/10.1002/mana.201300085