We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound.As...We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound.As an application we show that the Coleman–Oort conjecture holds for Shimura curves associated with partial corestriction upon a suitable choice of parameters,which generalizes a construction due to Mumford.展开更多
For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it...For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it follows from Deligne and Mostow(Publ.Math.IHÉS,63:5-89,1986)and Mostow(Publ.Math.IHÉS,63:91-106,1986;J.Am.Math.Soc.,1(3):555-586,1988)that,for n=3,it can be partially compactified to a Shimura family of ball type,and for n=5,9,there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.展开更多
基金supported by SFB/Transregio 45 Periods,Moduli Spaces and Arithmetic of Algebraic Varieties of DFG,by NSF of China Grant Nos.11771203,11231003,11301495Fundamental Research Funds for the Central Universities,Nanjing University,No.0203-14380009by the Science Foundation of Shanghai(No.13DZ2260400).
文摘We prove that a Shimura curve in the Siegel modular variety is not generically contained in the open Torelli locus as long as the rank of unitary part in its canonical Higgs bundle satisfies a numerical upper bound.As an application we show that the Coleman–Oort conjecture holds for Shimura curves associated with partial corestriction upon a suitable choice of parameters,which generalizes a construction due to Mumford.
文摘For each natural odd number n≥3,we exhibit a maximal family of n-dimensional Calabi-Yau manifolds whose Yukawa coupling length is 1.As a consequence,Shafarevich’s conjecture holds true for these families.Moreover,it follows from Deligne and Mostow(Publ.Math.IHÉS,63:5-89,1986)and Mostow(Publ.Math.IHÉS,63:91-106,1986;J.Am.Math.Soc.,1(3):555-586,1988)that,for n=3,it can be partially compactified to a Shimura family of ball type,and for n=5,9,there is a sub Q-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.
