An algebraic C 2-equivariant Bézout theorem

Abstract

One interpretation of Bézout’s theorem, nonequivariantly, is as a calculation of the Euler class of a sum of line bundles over complex projective space, expressing it in terms of the rank of the bundle and its degree. We generalize this calculation to the C2 –equivariant context, using the calculation of the cohomology of C2 –complex projective spaces from an earlier paper, which used ordinary C2 –cohomology with Burnside ring coefficients and an extended grading necessary to define the Euler class. We express the Euler class in terms of the equivariant rank of the bundle and the degrees of the bundle and its fixed subbundles. We do similar calculations using constant Z coefficients and Borel cohomology and compare the results. © 2024 MSP (Mathematical Sciences Publishers).