Details
| Original language | English |
|---|---|
| Article number | 22 |
| Number of pages | 16 |
| Journal | Research in Mathematical Sciences |
| Volume | 8 |
| Issue number | 2 |
| Publication status | Published - 12 Apr 2021 |
Abstract
Given d∈ N, we prove that any polarized Enriques surface (over any field k of characteristic p≠ 2 or with a smooth K3 cover) of degree greater than 12 d2 contains at most 12 rational curves of degree at most d. For d> 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.
Keywords
- Enriques surface, Genus one fibration, Hyperbolic lattice, Parabolic lattice, Polarization, Rational curve
ASJC Scopus subject areas
- Mathematics(all)
- Theoretical Computer Science
- Mathematics(all)
- Mathematics (miscellaneous)
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Research in Mathematical Sciences, Vol. 8, No. 2, 22, 12.04.2021.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Twelve Rational curves on Enriques surfaces
AU - Rams, Sławomir
AU - Schütt, Matthias
N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. Research partially supported by the National Science Centre, Poland, Opus Grant No. 2017/25/B/ST1/00853 (S. Rams).
PY - 2021/4/12
Y1 - 2021/4/12
N2 - Given d∈ N, we prove that any polarized Enriques surface (over any field k of characteristic p≠ 2 or with a smooth K3 cover) of degree greater than 12 d2 contains at most 12 rational curves of degree at most d. For d> 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.
AB - Given d∈ N, we prove that any polarized Enriques surface (over any field k of characteristic p≠ 2 or with a smooth K3 cover) of degree greater than 12 d2 contains at most 12 rational curves of degree at most d. For d> 2 , we construct examples of Enriques surfaces of high degree that contain exactly 12 rational degree-d curves.
KW - Enriques surface
KW - Genus one fibration
KW - Hyperbolic lattice
KW - Parabolic lattice
KW - Polarization
KW - Rational curve
UR - http://www.scopus.com/inward/record.url?scp=85104322227&partnerID=8YFLogxK
U2 - 10.1007/s40687-021-00262-7
DO - 10.1007/s40687-021-00262-7
M3 - Article
AN - SCOPUS:85104322227
VL - 8
JO - Research in Mathematical Sciences
JF - Research in Mathematical Sciences
SN - 2522-0144
IS - 2
M1 - 22
ER -