A degree bound for families of rational curves on surfaces

Niels Lubbes

doi:10.1016/j.jpaa.2018.02.033

A degree bound for families of rational curves on surfaces

Niels Lubbes

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.

Original language	English (US)
Pages (from-to)	30-47
Number of pages	18
Journal	Journal of Pure and Applied Algebra
Volume	223
Issue number	1
DOIs	https://doi.org/10.1016/j.jpaa.2018.02.033
State	Published - Jan 2019
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2021-03-11
Acknowledgements: I would like to thank Josef Schicho for useful discussions. This work was supported by base funding of the King Abdullah University of Science and Technology.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jpaa.2018.02.033

Cite this

@article{3e7891735a754f4f8c55776ffa36d9a6,

title = "A degree bound for families of rational curves on surfaces",

abstract = "We give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.",

author = "Niels Lubbes",

note = "KAUST Repository Item: Exported on 2021-03-11 Acknowledgements: I would like to thank Josef Schicho for useful discussions. This work was supported by base funding of the King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2019",

month = jan,

doi = "10.1016/j.jpaa.2018.02.033",

language = "English (US)",

volume = "223",

pages = "30--47",

journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - A degree bound for families of rational curves on surfaces

AU - Lubbes, Niels

N1 - KAUST Repository Item: Exported on 2021-03-11 Acknowledgements: I would like to thank Josef Schicho for useful discussions. This work was supported by base funding of the King Abdullah University of Science and Technology. This publication acknowledges KAUST support, but has no KAUST affiliated authors.

PY - 2019/1

Y1 - 2019/1

N2 - We give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.

AB - We give an upper bound for the degree of rational curves in a family that covers a given birationally ruled surface in projective space. The upper bound is stated in terms of the degree, sectional genus and arithmetic genus of the surface. We introduce an algorithm for constructing examples where the upper bound is tight. As an application of our methods we improve an inequality on lattice polygons.

UR - http://hdl.handle.net/10754/668052

UR - https://linkinghub.elsevier.com/retrieve/pii/S0022404918300513

UR - http://www.scopus.com/inward/record.url?scp=85042644296&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2018.02.033

DO - 10.1016/j.jpaa.2018.02.033

M3 - Article

SN - 0022-4049

VL - 223

SP - 30

EP - 47

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 1

ER -

A degree bound for families of rational curves on surfaces

Abstract

Bibliographical note

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this