TY - JOUR
A2 - Saidi, E. H.
A2 - Franco, D.
AU - Momot, Aleksander
PY - 2011
DA - 2011/06/19
TI - On Modular Ball-Quotient Surfaces of Kodaira Dimension One
SP - 214853
VL - 2011
AB - Let Γ⊂PU(2,1) be a lattice which is not co-ompact, of finite covolume with respect to the Bergman metric and acting freely on the open unit ball B⊂ℂ2. Thenthe toroidal compactification X=Γ\B¯ is a projective smooth surface with elliptic compactification divisor D=X\(Γ\B). In this short note wediscover a new class of unramifed ball quotients X. We consider ball quotientsX with kod(X)=1 and h1(X,𝒪X)=1. We prove that each minimal surfacewith finite Mordell-Weil group in the class described admits an étale coveringwhich is a pull-back of X6(6). Here X6(6) denotes the elliptic modular surfaceparametrizing elliptic curves E with 6-torsion points x,y which generate E[6].
SN - xxxx-xxxx
UR - https://doi.org/10.5402/2011/214853
DO - 10.5402/2011/214853
JF - ISRN Geometry
PB - International Scholarly Research Network
KW -
ER -