Arrangement of hyperplanes I: Rational functions and Jeffrey-Kirwan residue
نویسندگان
چکیده
Consider the space R∆ of rational functions of r variables with poles on an arrangement of hyperplanes ∆. It is important to study the decomposition of the space R∆ under the action of the ring of differential operators with constant coefficients. In the one variable case, a rational function of z with poles at most on z = 0 is written uniquely as φ(z) = Princ(φ)(z)+ψ(z) where Princ(φ)(z) = ∑ n<0 anz n is the principal part of φ(z) and ψ(z) = ∑ n≥0 anz n is the polynomial part of φ(z). Remark that the space
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