We present a formula for computing proper pushforwards of classes in the Chow ring of a projective bundle under the projection $\pi :{\mathbb {P}}(\mathscr{E})\rightarrow B$, for B being a non-singular 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.
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2011
American Institute of Physics
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