0000000000799125

AUTHOR

Sheng-li Tan

showing 2 related works from this author

On Higgs bundles over Shimura varieties of ball quotient type

2016

We prove the generic exclusion of certain Shimura varieties of unitary and orthogonal types from the Torelli locus. The proof relies on a slope inequality on surface fibration due to G. Xiao, and the main result implies that certain Shimura varieties only meet the Torelli locus in dimension zero.

Pure mathematicsMathematics - Number TheoryApplied MathematicsGeneral MathematicsMathematics::Number Theory010102 general mathematicsFibrationQuotient type01 natural sciencesUnitary stateMathematics::Algebraic TopologyMathematics - Algebraic GeometryMathematics::Algebraic GeometryFOS: MathematicsHiggs bosonNumber Theory (math.NT)Ball (mathematics)0101 mathematicsMathematics::Representation TheoryAlgebraic Geometry (math.AG)Mathematics
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On the minimal number of singular fibers with non-compact Jacobians for families of curves over P1

2016

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.

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 fieldMathematicsJournal de Mathématiques Pures et Appliquées
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