6533b850fe1ef96bd12a816e
RESEARCH PRODUCT
On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1
Xin LuXin LuSheng-li TanWan-yuan XuKang Zuosubject
0301 basic medicineDiscrete mathematicsPure mathematicsApplied MathematicsGeneral Mathematics010102 general mathematics01 natural sciences03 medical and health sciencessymbols.namesakeMathematics::Algebraic Geometry030104 developmental biologyGenus (mathematics)Jacobian matrix and determinantFamily of curvessymbols0101 mathematicsAlgebraically closed fieldMathematicsdescription
Abstract Let f : X → P 1 be a non-isotrivial family of semi-stable curves of genus g ≥ 1 defined over an algebraically closed field k. Denote by s nc the number of the singular fibers whose Jacobians are non-compact. We prove that s nc ≥ 5 if k = C and g ≥ 5 ; we also prove that s nc ≥ 4 if char ( k ) > 0 and the relative Jacobian of f is non-smooth.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-05-01 | Journal de Mathématiques Pures et Appliquées |