Applications of algebraic analysis to geometry

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We studied Lefschetz fixed point formulas for maps with higher-dimensional fixed point sets and obtained a formula which expresses their fixed point indices explicitly. We also obtained formulas describing the dimensions and the degrees of A-discriminant varieties introduced by Gelfand etc. in terms of the geometric data of the configuration A.Moreover, as byproducts of this research, various results on the monodromies at infinity of polynomial maps, the analytic continuations of A-hypergeometric functions and the poles of local zeta functions etc. are also obtained.