Seshadri constants, gonality of space curves, and restriction of stable bundles

Paoletti, Roberto

doi:10.4310/jdg/1214455776

Cited by 12 publications

(12 citation statements)

References 27 publications

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“…If the surface contains a line, and the curve is either in the biliaison class of the line, or residual to the line, then the line becomes a multisecant of high order that computes the gonality. This case was also observed by Paoletti [16].…”

Section: Resultssupporting

confidence: 81%

Clifford Index of ACM Curves in P 3

Hartshorne

2002

Milan Journal of Mathematics

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In this paper we review the notions of gonality and Clifford index of an abstract curve. For a curve embedded in a projective space, we investigate the connection between the Clifford index of the curve and the geometrical properties of its embedding . In particular if C is a curve of degree d in P 3 , and if L is a multisecant of maximum order k , then the pencil of planes through L cuts outIf the gonality of C is equal to d − k we say the gonality of C can be computed by multisecants. We discuss the question whether the gonality of every smooth ACM curve in P 3 can be computed by multisecants, and we show the answer is yes in some special cases.

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Section: Resultssupporting

confidence: 81%

Clifford Index of ACM Curves in P 3

Hartshorne

2002

Milan Journal of Mathematics

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“…Then Paoletti [25], p. 487, shows that the s-invariant t H (J ) has a simple geometric interpretation, as follows. Consider first a non-constant mapping f :…”

Section: Remark 19 (Paoletti's Geometric Interpretation Of the S-inmentioning

confidence: 99%

Positivity and complexity of ideal sheaves

Cutkosky¹,

Ein²,

Lazarsfeld³

2001

Mathematische Annalen

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“…With respect to this example, it should be remarked that, in general, for some curve and some integer e, describing all linear systems g 1 e on that curve is a very difficult problem. For example, determining the gonality of space curves is already a difficult problem (see, e.g., Paoletti, 1994).…”

Section: Introductionmentioning

confidence: 99%

Curves Having Schemes of Special Linear Systems with Multiple Components

Coppens

2008

Communications in Algebra

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In this article, we show that it is of frequent occurrence that smooth curves do have multiple components for some of their schemes W 1 e of special divisors. For a smooth space curve C of degree d, we give sufficient conditions implying that W 1 d−2 has a multiple component, and we prove the existence of many space curves satisfying those conditions. As an example of a more general result for curves in r , we prove that general complete intersection curves of degree d in 4 do have multiple components for the schemes W 1 d−5 and W 1 d−4 .

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Seshadri constants, gonality of space curves, and restriction of stable bundles

Cited by 12 publications

References 27 publications

Clifford Index of ACM Curves in P 3

Clifford Index of ACM Curves in P 3

Positivity and complexity of ideal sheaves

Curves Having Schemes of Special Linear Systems with Multiple Components

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