Let M be an open Riemann surface with a finite set of punctures, a complete Poincar(?)-like metric is introduced near the punctures and the equivalence between the stability of an indecomposable parabolic Higgs bundle...Let M be an open Riemann surface with a finite set of punctures, a complete Poincar(?)-like metric is introduced near the punctures and the equivalence between the stability of an indecomposable parabolic Higgs bundle, and the existence of a Hermitian-Einstein metric on the bundle is established.展开更多
In this paper,we prove a Chern number inequality for Higgs bundles over some Kähler manifolds.As an application,we get the Bogomolov inequality for semi-stable parabolic Higgs bundles over smooth projective varie...In this paper,we prove a Chern number inequality for Higgs bundles over some Kähler manifolds.As an application,we get the Bogomolov inequality for semi-stable parabolic Higgs bundles over smooth projective varieties.展开更多
Let V be an asymptotically cylindrical Kahler manifold with asymptotic cross-section ■. Let (E■,Φ■)be a st able Higgs bundle over ■, and (E,Φ) a Higgs bundle over V which is asymptotic to (E■,Φ■). In this pap...Let V be an asymptotically cylindrical Kahler manifold with asymptotic cross-section ■. Let (E■,Φ■)be a st able Higgs bundle over ■, and (E,Φ) a Higgs bundle over V which is asymptotic to (E■,Φ■). In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant projectively Hermitian Yang-Mills metric on (E,Φ).展开更多
In this paper,we consider the stability,semi-stability and canonical metric structures on transverse Higgs bundles over a class of foliation manifolds.Also a transversal Bogomolov inequality is obtained.
In this note we will introduce our recent work on the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles, and the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at in...In this note we will introduce our recent work on the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles, and the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity.展开更多
We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to...We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.展开更多
The p-adic Simpson correspondence due to Faltings(Adv Math 198(2):847-862,2005)is a p-adic analogue of non-abelian Hodge theory.The following is the main result of this article:The correspondence for line bundles can ...The p-adic Simpson correspondence due to Faltings(Adv Math 198(2):847-862,2005)is a p-adic analogue of non-abelian Hodge theory.The following is the main result of this article:The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli spaces under certain smallness conditions.In the complex setting,Simpson shows that there is a complex analytic morphism from the moduli space for the vector bundles with integrable connection to the moduli space of representations of a finitely generated group as algebraic varieties.We give a p-adic analogue of Simpson’s result.展开更多
In this article,we give an explicit way to construct representations of thefundamental groupπ_(1)(X),where X is a hyperbolic curve over C.Our motivation isto study a special space in MDR(X,SL_(2)(C))which is called t...In this article,we give an explicit way to construct representations of thefundamental groupπ_(1)(X),where X is a hyperbolic curve over C.Our motivation isto study a special space in MDR(X,SL_(2)(C))which is called the space of permissibleconnections in Faltings(Compos Math 48(2):223-269,1983),or indigenous bundlesin Gunning(Math Ann 170:67-86,1967).We get representations by constructingHiggs bundles,and we show that the family we get intersects the space of permissibleconnections PC in a positive dimension.In this way,we actually get a deformation ofthe canonical representation in PC,and all these deformations are given by explicitconstructed Higgs bundles.We also estimate the dimension of this deformation space.展开更多
The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence betwee...The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence between the moduli space of semi-simple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers.In this paper,we extend this correspondence to the projectively flat bundles over some non-Kahler manifold cases.Firstly,we prove an existence theorem of Poisson metrics on simple projectively flat bundles over compact Hermitian manifolds.As its application,we obtain a vanishing theorem of characteristic classes of projectively flat bundles.Secondly,on compact Hermitian manifolds which satisfy Gauduchon and astheno-K?hler conditions,we combine the continuity method and the heat flow method to prove that every semi-stable Higgs bundle withΔ(E,?E)·[ωn-2]=0 must be an extension of stable Higgs bundles.Using the above results,over some compact non-Kahler manifolds(M,ω),we establish an equivalence of categories between the category of semi-stable(poly-stable)Higgs bundles(E,?E,φ)withΔ(E,?E)·[ωn-2]=0 and the category of(semi-simple)projectively flat bundles(E,D)with(-1)(1/2)FD=α■IdE for some real(1,1)-formα.展开更多
Let f ： X → U be a family of smooth hypersurfaces in P nof degree d ＆gt; n＋1 over a smooth curve U.Assume that the Griffiths-Yukawa coupling of f is non-vanishing.Then f is rigid.Moreover,we generalize it to the c...Let f ： X → U be a family of smooth hypersurfaces in P nof degree d ＆gt; n＋1 over a smooth curve U.Assume that the Griffiths-Yukawa coupling of f is non-vanishing.Then f is rigid.Moreover,we generalize it to the case when the Griffiths-Yukawa coupling of f is degenerated.展开更多
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
基金Project surpported partially by the National Natural Science Foundation of China (Grant No. 19701034).
文摘Let M be an open Riemann surface with a finite set of punctures, a complete Poincar(?)-like metric is introduced near the punctures and the equivalence between the stability of an indecomposable parabolic Higgs bundle, and the existence of a Hermitian-Einstein metric on the bundle is established.
文摘In this paper,we prove a Chern number inequality for Higgs bundles over some Kähler manifolds.As an application,we get the Bogomolov inequality for semi-stable parabolic Higgs bundles over smooth projective varieties.
基金partially supported by NSF in China(Grant Nos.11625106,11571332 and 11721101)
文摘Let V be an asymptotically cylindrical Kahler manifold with asymptotic cross-section ■. Let (E■,Φ■)be a st able Higgs bundle over ■, and (E,Φ) a Higgs bundle over V which is asymptotic to (E■,Φ■). In this paper, using the continuity method of Uhlenbeck and Yau, we prove that there exists an asymptotically translation-invariant projectively Hermitian Yang-Mills metric on (E,Φ).
基金supported by National Natural Science Foundation of China(Grant Nos.11625106,11571332 and 11721101)。
文摘In this paper,we consider the stability,semi-stability and canonical metric structures on transverse Higgs bundles over a class of foliation manifolds.Also a transversal Bogomolov inequality is obtained.
文摘In this note we will introduce our recent work on the existence of approximate Hermitian-Einstein structures on semi-stable Higgs bundles, and the asymptotic behavior of the Yang-Mills-Higgs flow for Higgs pairs at infinity.
基金supported by National Natural Science Foundation of China(Grant Nos.11101393 and 11201447)
文摘We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.
文摘The p-adic Simpson correspondence due to Faltings(Adv Math 198(2):847-862,2005)is a p-adic analogue of non-abelian Hodge theory.The following is the main result of this article:The correspondence for line bundles can be enhanced to a rigid analytic morphism of moduli spaces under certain smallness conditions.In the complex setting,Simpson shows that there is a complex analytic morphism from the moduli space for the vector bundles with integrable connection to the moduli space of representations of a finitely generated group as algebraic varieties.We give a p-adic analogue of Simpson’s result.
文摘In this article,we give an explicit way to construct representations of thefundamental groupπ_(1)(X),where X is a hyperbolic curve over C.Our motivation isto study a special space in MDR(X,SL_(2)(C))which is called the space of permissibleconnections in Faltings(Compos Math 48(2):223-269,1983),or indigenous bundlesin Gunning(Math Ann 170:67-86,1967).We get representations by constructingHiggs bundles,and we show that the family we get intersects the space of permissibleconnections PC in a positive dimension.In this way,we actually get a deformation ofthe canonical representation in PC,and all these deformations are given by explicitconstructed Higgs bundles.We also estimate the dimension of this deformation space.
基金supported by the National Key R&D Program of China(Grant No.2020YFA0713100)National Natural Science Foundation of China(Grant Nos.12141104,11801535,11721101and 11625106)。
文摘The non-abelian Hodge correspondence was established by Corlette(1988),Donaldson(1987),Hit chin(1987)and Simpson(1988,1992).It states that on a compact Kahler manifold(X,ω),there is a one-to-one correspondence between the moduli space of semi-simple flat complex vector bundles and the moduli space of poly-stable Higgs bundles with vanishing Chern numbers.In this paper,we extend this correspondence to the projectively flat bundles over some non-Kahler manifold cases.Firstly,we prove an existence theorem of Poisson metrics on simple projectively flat bundles over compact Hermitian manifolds.As its application,we obtain a vanishing theorem of characteristic classes of projectively flat bundles.Secondly,on compact Hermitian manifolds which satisfy Gauduchon and astheno-K?hler conditions,we combine the continuity method and the heat flow method to prove that every semi-stable Higgs bundle withΔ(E,?E)·[ωn-2]=0 must be an extension of stable Higgs bundles.Using the above results,over some compact non-Kahler manifolds(M,ω),we establish an equivalence of categories between the category of semi-stable(poly-stable)Higgs bundles(E,?E,φ)withΔ(E,?E)·[ωn-2]=0 and the category of(semi-simple)projectively flat bundles(E,D)with(-1)(1/2)FD=α■IdE for some real(1,1)-formα.
文摘Let f ： X → U be a family of smooth hypersurfaces in P nof degree d ＆gt; n＋1 over a smooth curve U.Assume that the Griffiths-Yukawa coupling of f is non-vanishing.Then f is rigid.Moreover,we generalize it to the case when the Griffiths-Yukawa coupling of f is degenerated.
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.
