1999
DOI: 10.1007/bf02940883
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Normal generation of line bundles of high degrees on smooth algebraic curves

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Cited by 12 publications
(8 citation statements)
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“…And we obtain a result for the case deg L = 2g − 6 as its corollary and apply this result to the known cases of 2g [10]). …”
Section: Introductionmentioning
confidence: 80%
See 1 more Smart Citation
“…And we obtain a result for the case deg L = 2g − 6 as its corollary and apply this result to the known cases of 2g [10]). …”
Section: Introductionmentioning
confidence: 80%
“…In fact, Kato, Keem, and Ohbuchi in [10] determined the conditions for non-special very ample line bundles of degree 2g − 2, 2g − 3 failing to be normally generated. Also the conditions for the cases of degree 2g − 4, 2g − 5 are known in [9].…”
Section: Introductionmentioning
confidence: 99%
“…Consequently, L is very ample with h 1 (C, L) = 1, whence c : 4. According to Theorem 15, L fails to be normally generated, since the assumption g > (n − 1)(nd − 6) + ng(C ) implies deg L = 2g − nd + 5 3g 2 − 1 and so h 1 (C, L 2 (− 7 i=1 P i )) = 0.…”
Section: For a Linear Series G R D On C And Effective Divisors B I Onmentioning
confidence: 91%
“…The line bundles of degree 2g−1 which are not normally generated are fully ÿgured out by Corollary 1.6 in [4]. The normal generation of nonspecial line bundles of degrees 2g − 2 and 2g − 3 were dealt in [7]. Therefore we investigate the normal generation of nonspecial line bundles of degrees 2g − 4 and 2g − 5 in this paper.…”
Section: Normal Generation Of Nonspecial Line Bundlesmentioning
confidence: 94%
“…It has shown that the canonical line bundle on a nonhyperelliptic curve is normally generated [11]. Recently Kato, Keem, and Ohbuchi, gave the necessary and su cient conditions for nonspecial very ample line bundles of degrees 2g − 2, 2g − 3 and also for special line bundles of degree d ¿ 2g − 6 being normally generated [7]. In this paper we determine the conditions that nonspecial very ample line bundles of degrees 2g − 4; 2g − 5, or special line bundles of degree 2g − 7 on a smooth curve are normally generated.…”
Section: Introductionmentioning
confidence: 99%