Families of abelian varieties over curves with maximal Higgs field
| dc.creator | Viehweg, Eckart | |
| dc.creator | Zuo, Kang | |
| dc.date | 2002-04-22 | |
| dc.date | 2002-07-25 | |
| dc.date.accessioned | 2026-07-07T04:47:58Z | |
| dc.date.available | 2026-07-07T04:47:58Z | |
| dc.description | Let f:X-->Y be a semi-stable family of complex abelian varieties over a curve Y of genus q, and smooth over the complement of s points. If F(1,0) denotes the non-flat (1,0) part of the corresponding variation of Hodge structures, the Arakelov inequalities say that 2deg(F(1,0)) is bounded from above by g=rank(F(1,0))(2q-2+s). We show that for s>0 families reaching this bound are isogenous to the g-fold product of a modular family of elliptic curves, and a constant abelian variety. The content of this note became part of the article "A characterization of certain Shimura curves in the moduly stack of abelian varieties" (math.AG/0207228), where we also handle the case s=0. | |
| dc.description | 13 pages, Latex, two minor errors corrected, the content of this note became part of math.AG/0207228 | |
| dc.identifier | https://arxiv.org/abs/math/0204261 | |
| dc.identifier | http://arxiv.org/abs/math/0204261 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63874 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14K10 (Primary) 14D05, 14D07 (Secondary) | |
| dc.title | Families of abelian varieties over curves with maximal Higgs field | |
| dc.type | text |