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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-18 |
| Number of pages | 18 |
| Journal | Journal of Algebra |
| Volume | 497 |
| DOIs | |
| 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
Bisecant and trisecant curves on ruled surfaces. / Choe, Insong; Choi, Youngook; Kim, Seonja; Park, Euisung.
In: Journal of Algebra, Vol. 497, 01.03.2018, p. 1-18.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bisecant and trisecant curves on ruled surfaces
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 - http://www.scopus.com/inward/record.url?scp=85034595826&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85034595826&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2017.11.017
DO - 10.1016/j.jalgebra.2017.11.017
M3 - Article
AN - SCOPUS:85034595826
VL - 497
SP - 1
EP - 18
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -