Families of K3 surfaces over curves satisfying the equality of Arakelov-Yau's type and modularity
| dc.creator | Sun, Xiaotao | |
| dc.creator | Tan, Sheng-Li | |
| dc.creator | Zuo, Kang | |
| dc.date | 2002-05-20 | |
| dc.date.accessioned | 2026-07-07T04:48:36Z | |
| dc.date.available | 2026-07-07T04:48:36Z | |
| dc.description | Let $f:X\to C$ be a family of semistable K3 surfaces with non-empty set $S$ of singular fibres having infinite local monodromy. Then, when the so called Arakelov-Yau inequality reaches equality, we prove that $C\setminus S$ is a modular curve and the family comes essentially from a family of elliptic curves through a so called Nikulin-Kummer construction. In particular, when $C=\BBb P^1$, the family of elliptic curves must be one of Beauville's 6 examples where Arakelov inequality reaches equality. | |
| dc.description | 18 pages, Latex | |
| dc.identifier | https://arxiv.org/abs/math/0205213 | |
| dc.identifier | http://arxiv.org/abs/math/0205213 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64110 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Families of K3 surfaces over curves satisfying the equality of Arakelov-Yau's type and modularity | |
| dc.type | text |