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

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

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Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

Choe, I., Choi, Y., Kim, S., & Park, E. (2018). Bisecant and trisecant curves on ruled surfaces. Journal of Algebra, 497, 1-18. https://doi.org/10.1016/j.jalgebra.2017.11.017

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10.1016/j.jalgebra.2017.11.017