A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of ...A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.But in general a toric origami manifold is not simply connected,so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold.In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template.Furthermore,they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.展开更多
In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological...Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological smoothability criterion for normal crossings symplectic varieties.The present paper constructs a blowup,a complex line bundle,and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle.These structures have applications in constructions and analysis of various moduli spaces.As a corollary of the Chern class formula for the logarithmic tangent bundle,we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.展开更多
Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a ...Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a nowhere vanishing section.It is proved that in case dim(X)≥3,π*(E)is trivial if and only if E is filtrable by vector bundles.With the structure theorem,the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.展开更多
In this note, we present a connection between equivariant Bott–Chern classesand K?hler–Ricci solitons. We also propose a generalized version the of the K–energy.
基金supported by the National Natural Science Foundation of China(Nos.11801186,11901218)。
文摘A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic manifold.For a toric symplectic manifold,its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.But in general a toric origami manifold is not simply connected,so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic manifold.In this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami template.Furthermore,they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.
文摘In this article,we give a further survey of some progress of the applications of group actions in the complex geometry after my earlier survey around 2020,mostly related to my own interests.
基金Supported by NSF grants DMS-2003340(F.Tehrani)DMS-1811861(Mclean)DMS-1901979(Zinger)。
文摘Our previous papers introduce topological notions of normal crossings symplectic divisor and variety,show that they are equivalent,in a suitable sense,to the corresponding geometric notions,and establish a topological smoothability criterion for normal crossings symplectic varieties.The present paper constructs a blowup,a complex line bundle,and a logarithmic tangent bundle naturally associated with a normal crossings symplectic divisor and determines the Chern class of the last bundle.These structures have applications in constructions and analysis of various moduli spaces.As a corollary of the Chern class formula for the logarithmic tangent bundle,we refine Aluffi’s formula for the Chern class of the tangent bundle of the blowup at a complete intersection to account for the torsion and extend it to the blowup at the deepest stratum of an arbitrary normal crossings divisor.
基金supported by the National Natural Science Foundation of China(Nos.11671330,11688101,11431013).
文摘Let X be a Hopf manifold with non-Abelian fundamental group and E be a holomorphic vector bundle over X,with trivial pull-back to C^n-{0}.The authors show that there exists a line bundle L over X such that E■L has a nowhere vanishing section.It is proved that in case dim(X)≥3,π*(E)is trivial if and only if E is filtrable by vector bundles.With the structure theorem,the authors get the cohomology dimension of holomorphic bundle E over X with trivial pull-back and the vanishing of Chern class of E.
基金Supported partially by NSF grants and a Simons fund
文摘In this note, we present a connection between equivariant Bott–Chern classesand K?hler–Ricci solitons. We also propose a generalized version the of the K–energy.
