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

Department of Mathematics

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

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

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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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.

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KW - Ruled surfaces

KW - Segre invariants

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