Neighborhood of a Rational Curve with a Node

Ueda, Tetsuo

doi:10.2977/prims/1195169425

Cited by 6 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Refining this technique by considering the exterior derivatives of such 0-cochains, we prove Theorem 1.4. [U83,Theorem 1,2] and [U91,Theorem 1,2] are shown by constructing a suitable function Φ λ on a neighborhood of the curve for each λ > 0. We prove Theorem 1.5 and Theorem 1.6 by generalizing this construction.…”

Section: Introductionmentioning

confidence: 99%

Ueda theory for compact curves with nodes

Koike¹

2017

Indiana Univ. Math. J.

View full text Add to dashboard Cite

Abstract. Let C be a compact complex curve included in a non-singular complex surface such that the normal bundle is topologically trivial. Ueda studied complex analytic properties of a neighborhood of C when C is non-singular or is a rational curve with a node. We propose an analogue of Ueda's theory for the case where C admits nodes. As an application, we study singular Hermitian metrics with semi-positive curvature on the anti-canonical bundle of the blow-up of the projective plane at nine points in arbitrary position.

show abstract

Section: Introductionmentioning

confidence: 99%

Ueda theory for compact curves with nodes

Koike¹

2017

Indiana Univ. Math. J.

View full text Add to dashboard Cite

show abstract

“…Lemma 3.14. (Lemma 5 of [11]) Let X be a smooth compact complex surface, K a compact subset of X and B be a holomorphic vector bundle over X. If X −K is strictly pseudoconvex, then every section s of B over X −K can be extended as a meromorphic sections over all X.…”

Section: Foliations With Q-gorenstein Normal Bundlementioning

confidence: 99%

Invariant curves for holomorphic foliations on singular surfaces

Santos

2020

Arkiv För Matematik

View full text Add to dashboard Cite

The Separatrix Theorem of C. Camacho and P. Sad says that there exists at least one invariant curve (separatrix) passing through the singularity of a germ of holomorphic foliation on complex surface, when the surface underlying the foliation is smooth or when it is singular and the dual graph of resolution surface singularity is a tree. Under some assumptions, we obtain existence of separatrix even when the resolution dual graph of the surface singular point is not a tree. It will be necessary to require an extra condition of the foliation, namely, absence of saddle-node in its reduction of singularities.In 1988, C. Camacho showed in [3] an extension of this result to include foliations on some singular surfaces:The author would like to thanks J. V. Pereira for incentive, valuable ideas and conversations.

show abstract

On the formal principle for curves on projective surfaces

Pereira

Thom

2020

Math. Ann.

View full text Add to dashboard Cite

Neighborhood of a Rational Curve with a Node

Cited by 6 publications

References 8 publications

Ueda theory for compact curves with nodes

Ueda theory for compact curves with nodes

Invariant curves for holomorphic foliations on singular surfaces

On the formal principle for curves on projective surfaces

Contact Info

Product

Resources

About