Genera of algebraic varieties and counting of lattice points
Genera of algebraic varieties and counting of lattice points
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代数簇的属和格点计数
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
J. Shaneson
中科院分区：
文献类型：
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作者：
S. Cappell;J. Shaneson
本文宣布结果的行为，一些重要的代数和拓扑不变量-欧拉特征，算术属，和他们的交叉同源类似物;签名等-和他们的相关特征类，下态射的投射代数簇。所得到的公式涉及到一般复代数（或解析）映射的奇异性的全球不变量。这些结果，新的，甚至复杂的流形，适用于获得一个版本的Grothendieck-Riemann-Roch，计算的托德类的环面品种，并明确的公式，在一个多胞形在欧氏空间中的整顶点。
This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas obtained relate global invariants to singularities of general complex algebraic (or analytic) maps. These results, new even for complex manifolds, are applied to obtain a version of Grothendieck-Riemann-Roch, a calculation of Todd classes of toric varieties, and an explicit formula for the number of integral points in a polytope in Euclidean space with integral vertices.