  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 hav
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.

Symplectic Geometry;High Energy Physics - Theory;Algebraic Geometry