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
We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family.This construction,motivated in part by the Gross-Siebert and B.Parke...We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family.This construction,motivated in part by the Gross-Siebert and B.Parker’s programs,contains a multifold version of the usual(two-fold)symplectic cut construction and in particular splits a symplectic manifold into several symplectic manifolds containing normal crossings symplectic divisors with shared irreducible components in one step.展开更多
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.
文摘We use local Hamiltonian torus actions to degenerate a symplectic manifold to a normal crossings symplectic variety in a smooth one-parameter family.This construction,motivated in part by the Gross-Siebert and B.Parker’s programs,contains a multifold version of the usual(two-fold)symplectic cut construction and in particular splits a symplectic manifold into several symplectic manifolds containing normal crossings symplectic divisors with shared irreducible components in one step.
