Bisecant and trisecant curves on ruled surfaces

Insong Choe; Youngook Choi; Seonja Kim; Euisung Park

doi:10.1016/j.jalgebra.2017.11.017

Bisecant and trisecant curves on ruled surfaces

Insong Choe
, Youngook Choi^*
, Seonja Kim
, Euisung Park

^*Corresponding author for this work

Department of Mathematics

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

1 Citation (Scopus)

Abstract

In this paper, we study numerical classes of integral curves on a ruled surface P(E) associated to a stable bundle E. The nef cone of a ruled surface is generated by the classes of a minimal section C₀ and a fiber f. We compute the smallest integer b such that the class kC₀+bf contains a multisecant curve for k=2 and 3. Also we find its consequence on the Lange stability of Sym^kE.

Original language	English
Pages (from-to)	1-18
Number of pages	18
Journal	Journal of Algebra
Volume	497
DOIs	https://doi.org/10.1016/j.jalgebra.2017.11.017
Publication status	Published - 2018 Mar 1

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Inc.

Keywords

Bisecant curves
Elementary transformation
Moduli of vector bundles
Ruled surfaces
Segre invariants
Trisecant curves

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2017.11.017

Cite this

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title = "Bisecant and trisecant curves on ruled surfaces",

abstract = "In this paper, we study numerical classes of integral curves on a ruled surface P(E) associated to a stable bundle E. The nef cone of a ruled surface is generated by the classes of a minimal section C0 and a fiber f. We compute the smallest integer b such that the class kC0+bf contains a multisecant curve for k=2 and 3. Also we find its consequence on the Lange stability of SymkE.",

keywords = "Bisecant curves, Elementary transformation, Moduli of vector bundles, Ruled surfaces, Segre invariants, Trisecant curves",

author = "Insong Choe and Youngook Choi and Seonja Kim and Euisung Park",

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doi = "10.1016/j.jalgebra.2017.11.017",

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AU - Choe, Insong

AU - Choi, Youngook

AU - Kim, Seonja

AU - Park, Euisung

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this paper, we study numerical classes of integral curves on a ruled surface P(E) associated to a stable bundle E. The nef cone of a ruled surface is generated by the classes of a minimal section C0 and a fiber f. We compute the smallest integer b such that the class kC0+bf contains a multisecant curve for k=2 and 3. Also we find its consequence on the Lange stability of SymkE.

AB - In this paper, we study numerical classes of integral curves on a ruled surface P(E) associated to a stable bundle E. The nef cone of a ruled surface is generated by the classes of a minimal section C0 and a fiber f. We compute the smallest integer b such that the class kC0+bf contains a multisecant curve for k=2 and 3. Also we find its consequence on the Lange stability of SymkE.

KW - Bisecant curves

KW - Elementary transformation

KW - Moduli of vector bundles

KW - Ruled surfaces

KW - Segre invariants

KW - Trisecant curves

UR - https://www.scopus.com/pages/publications/85034595826

U2 - 10.1016/j.jalgebra.2017.11.017

DO - 10.1016/j.jalgebra.2017.11.017

M3 - Article

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SN - 0021-8693

VL - 497

SP - 1

EP - 18

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Bisecant and trisecant curves on ruled surfaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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