Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 335-356 |
| Seitenumfang | 22 |
| Fachzeitschrift | Algebra and Number Theory |
| Jahrgang | 4 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 2010 |
Abstract
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Algebra and Number Theory, Jahrgang 4, Nr. 3, 2010, S. 335-356.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - K3 surfaces with Picard rank 20
AU - Schütt, Matthias
PY - 2010
Y1 - 2010
N2 - We determine all complex K3 surfaces with Picard rank 20 over ℚ. Here the Néron-Severi group has rank 20 and is generated by divisors which are defined over ℚ. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over ℚ is impossible for an elliptic K3 surface. We apply our methods to general singular K3 surfaces, that is, those with Néron-Severi group of rank 20, but not necessarily generated by divisors over ℚ.
AB - We determine all complex K3 surfaces with Picard rank 20 over ℚ. Here the Néron-Severi group has rank 20 and is generated by divisors which are defined over ℚ. Our proof uses modularity, the Artin-Tate conjecture and class group theory. With different techniques, the result has been established by Elkies to show that Mordell-Weil rank 18 over ℚ is impossible for an elliptic K3 surface. We apply our methods to general singular K3 surfaces, that is, those with Néron-Severi group of rank 20, but not necessarily generated by divisors over ℚ.
KW - Artin-Tate conjecture
KW - Class group
KW - Complex multiplication
KW - Modular form
KW - Singular K3 surface
UR - http://www.scopus.com/inward/record.url?scp=77953952264&partnerID=8YFLogxK
UR - https://arxiv.org/abs/0804.1558
U2 - 10.2140/ant.2010.4.335
DO - 10.2140/ant.2010.4.335
M3 - Article
AN - SCOPUS:77953952264
VL - 4
SP - 335
EP - 356
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 3
ER -