On generalized Sethi-Vafa-Witten formulas

We present a formula for computing proper pushforwards of classes in the Chow ring of a projective bundle under the projection pi : P(epsilon) -> B, for B being a nonsingular compact complex algebraic variety of any dimension. Our formula readily produces generalizations of formulas derived by Sethi, Vafa, and Witten to compute the Euler characteristic of elliptically fibered Calabi-Yau fourfolds used for F-theory compactifications of string vacua. The utility of such a formula is illustrated through applications, such as the ability to compute the Chern numbers of any non-singular complete intersection in such a projective bundle in terms of the Chern class of a line bundle on B. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3628633]