论文标题
chern-dold个性在复杂的山和theta除数中
Chern-Dold character in complex cobordisms and theta divisors
论文作者
论文摘要
我们表明，可以选择普通的主要两极化的阿贝尔品种的平滑theta分隔剂作为复杂恢复性中Chern-dold特征系数的不可还原代数代表，并描述Landweber-Novikov操作对它们的作用。我们将复杂的恢复理论的定量与双重网络诺维科夫代数作为变形参数空间，并表明Chern-dold特征可以解释为定量和去量图的组成。通过经典的Weierstrass椭圆函数来描述一些theta除数的平滑的现实分析代表。讨论了与Milnor-Hirzebruch问题有关可能的特征数量不可还原代数品种的联系。
We show that the smooth theta divisors of general principally polarised abelian varieties can be chosen as irreducible algebraic representatives of the coefficients of the Chern-Dold character in complex cobordisms and describe the action of the Landweber-Novikov operations on them. We introduce a quantisation of the complex cobordism theory with the dual Landweber-Novikov algebra as the deformation parameter space and show that the Chern-Dold character can be interpreted as the composition of quantisation and dequantisation maps. Some smooth real-analytic representatives of the cobordism classes of theta divisors are described in terms of the classical Weierstrass elliptic functions. The link with the Milnor-Hirzebruch problem about possible characteristic numbers of irreducible algebraic varieties is discussed.
