The base components of the dualizing sheaf of a curve on a surface

Konno, Kazuhiro; Lopes, Margarida Mendes

doi:10.1007/s00013-007-2555-y

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Lemma 27 Let C Be a Projective Curve Either Reduced With P1

Proposition 25 ( [5] Lemma 24 )1

Auxiliary Facts1

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Cited by 5 publications

(3 citation statements)

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“…Proof. The 1-connected case is treated in [14,Lemma 1.4]. We will apply the same arguments for the m-connected case with m ≥ 2.…”

Section: Lemma 27 Let C Be a Projective Curve Either Reduced With Pmentioning

confidence: 99%

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On Clifford's theorem for singular curves

Franciosi

Tenni

2013

Proceedings of the London Mathematical Society

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Let C be a 2-connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (i.e. a 0-dimensional scheme such that the space H 0 (C, I S K C ) contains a generically invertible section). Under some general assumptions on S or C we show that h 0 (C, I S K C ) ≤ p a (C) − 1 2 deg(S) and if equality holds then either S is trivial, or C is honestly hyperelliptic or 3-disconnected.As a corollary we give a generalization of Clifford's theorem for reduced curves with planar singularities.

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“…Proof. The 1-connected case is treated in [14,Lemma 1.4]. We will apply the same arguments for the m-connected case with m ≥ 2.…”

Section: Lemma 27 Let C Be a Projective Curve Either Reduced With Pmentioning

confidence: 99%

“…During our analysis of the curve C we will need to estimate the dimension of H 0 (A, O A ) for some subcurve A ⊂ C. To this purpose we give a slight generalization of a result of Konno and Mendes Lopes (see [14,Lemma 1.4]).…”

Section: Proposition 25 ( [5] Lemma 24 )mentioning

confidence: 99%

On Clifford's theorem for singular curves

Franciosi

Tenni

2013

Proceedings of the London Mathematical Society

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“…. This contradicts [KM,Lemma 1.4], that states that any subcurve D ′ of a 1-connected curve D satisfying…”

Section: Auxiliary Factsmentioning

confidence: 97%

A Characterization of the Symmetric Square of a Curve

Lopes

Pardini

Pirola

2012

International Mathematics Research Notices

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In this paper a new intrinsic geometric characterization of the symmetric square of a curve and of the ordinary product of two curves is given. More precisely it is shown that the existence on a surface of general type S of irregularity q of an effective divisor D having selfintersection D 2 > 0 and arithmetic genus q implies that S is either birational to a product of curves or to the second symmetric product of a curve.

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