  In light of Sen's weak coupling limit of F-theory as a type IIB orientifold,
the compatibility of the tadpole conditions leads to a non-trivial identity
relating the Euler characteristics of an elliptically fibered Calabi-Yau
fourfold and of certain related surfaces. We present the physical argument
leading to the identity, and a mathematical derivation of a Chern class
identity which confirms it, after taking into account singularities of the
relevant loci. This identity of Chern classes holds in arbitrary dimension, and
for varieties that are not necessarily Calabi-Yau. Singularities are essential
in both the physics and the mathematics arguments: the tadpole relation may be
interpreted as an identity involving stringy invariants of a singular
hypersurface, and corrections for the presence of pinch-points. The
mathematical discussion is streamlined by the use of Chern-Schwartz-MacPherson
classes of singular varieties. We also show how the main identity may be
obtained by applying `Verdier specialization' to suitable constructible
functions.
