On the minimal free resolution of curves of maximal regularity
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Let $C \subset \P^r$ 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.
Abstract
Let $C \subset \P^r$ 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.
참고문헌 (8)
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