Applications of algebraic analysis to geometry

研究了具有高维不动点集的映射的Lefschetz不动点公式，得到了一个显式表示其不动点指数的公式。我们还得到了由Gelfand等人引入的关于A-判别簇的维数和次数的公式.此外，作为研究的副产品，我们还得到了多项式映射无穷远点的单值性、A-超几何函数的解析延拓和局部zeta函数的极点等结果.

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.