Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON THE MINIMAL FREE RESOLUTION OF CURVES OF MAXIMAL REGULARITY

  • Lee, Wanseok (Department of Applied Mathematics Pukyong National University) ;
  • Park, Euisung (Department of Mathematics Korea University)
  • Received : 2015.10.30
  • Published : 2016.11.30
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Abstract

Let $C{\subset}{\mathbb{P}}^r$ be a nondegenerate projective curve of degree d > r + 1 and of maximal regularity. Such curves are always contained in the threefold scroll S(0, 0, r - 2). Also some of such curves are even contained in a rational normal surface scroll. In this paper we study the minimal free resolution of the homogeneous coordinate ring of C in the case where $d{\leq}2r-2$ and C is contained in a rational normal surface scroll. Our main result provides all the graded Betti numbers of C explicitly.

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References

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