Abstract.
Recall that a projective curve in \(\Bbb P^r\) with ideal sheaf \(\Cal I\) is said to be n-regular if \(H^i(\Bbb P^r, \Cal I\otimes\Cal O_{\Bbb P^r}(n-i))=0\) for every integer \(i>0\) and that in this case, it is cut out scheme-theoretically by equations of degree at most n. The purpose here is to show that an irreducible, reduced, projective curve of degree d and large arithmetic genus \(p_a\) satisfies a smaller regularity bound than the optimal one \(d-r+2\). For example, if \(p_a\geq r-2\) then a curve is \((d-2r+4)\)-regular unless it is embedded by a complete linear system of degree \(2p_a+2\).
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Received: 29 May 2000 / Published online: 24 September 2001
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Noma, A. A bound on the Castelnuovo-Mumford regularity for curves. Math Ann 322, 69–74 (2002). https://doi.org/10.1007/s002080100265
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DOI: https://doi.org/10.1007/s002080100265