On the Castelnuovo-Severi inequality for a double covering

Keem, Changho; Ohbuchi, Akira

doi:10.2969/aspm/05010269

Cited by 6 publications

(13 citation statements)

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“…(2) If either (a) b > 1 2 a(e + 4) + 5 2 , or (b) e is even and b > 1 2 a(e + 2) + 5 2 , then any pencil on X computing the gonality (and the Clifford index) is composed with π| X : X → E. Furthermore, if e 4 then these conclusions hold unless e = 4 and (a, b) = (2,8).…”

Section: Vol 84 2005mentioning

confidence: 98%

“…In addition s = α(2β − 5α) cannot be equal to 2, and so we have R e m a r k 2.9. Let X be any smooth curve of genus g with a bielliptic pencil X → E. Then X has a pencil g 1 g−1 not composed with the bielliptic structure (see [8]). In particular, a curve corresponding to the exceptional case of Theorem 2.4 (2) actually has a pencil of degree 4 not induced by any pencil on S.…”

Section: K S D Is Even For Any Divisor D On S)mentioning

confidence: 99%

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The gonality and the Clifford index of curves on an elliptic ruled surface

Harui

2005

Arch. Math.

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Abstract. Under certain numerical conditions, the gonality of curves on an elliptic ruled surface is twice the degree of the bundle map of the ruled surface and the Clifford index of such curves is computed by pencils of minimal degree. IntroductionThroughout this paper, a curve or a surface always means a projective, reduced and irreducible one over C. This is a non-negative integer by Clifford's Theorem. A divisor D is said to compute the Clifford index of X if D contributes to the Clifford index of X and satisfies that

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Section: Vol 84 2005mentioning

confidence: 98%

Section: K S D Is Even For Any Divisor D On S)mentioning

confidence: 99%

The gonality and the Clifford index of curves on an elliptic ruled surface

Harui

2005

Arch. Math.

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“…By the main result in [7], there exists a base-point-free and complete g 1 g−3 on X . Therefore we also have…”

Section: Double Coverings Of Low Genus Curvesmentioning

confidence: 99%

On double coverings of hyperelliptic curves

Ballico

Keem

2006

Journal of Pure and Applied Algebra

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“…3. If 0 ≤ s ≤ 2g and π ≥ 4g − s then there is a base-point-free pencil of degree d = π − 2g + 1 + s which is not composed with the given double covering (see [8]). Note, that these bounds implies d ≥ 2g + 1.…”

Section: Introductionmentioning

confidence: 99%

“…Note, that this fact was used by Keem and Ohbuchi in [8], but not exactly in the same way. They use the properties of the elementary transformations of ruled surfaces.…”

Section: Introductionmentioning

confidence: 99%