论文标题
关于歌手-HOPF猜想的单数变体
On singular variants of the Singer-Hopf Conjecture
论文作者
论文摘要
我们提出了歌手-HOPF猜想的奇异变体，该变体是根据Euler-Mather特征，相交的同源性特征和分子的，是封闭的非洲非球体亚球构成型射击传播的封闭不可减小的亚无subvariety的虚拟特征。我们证明了猜想的假设，即环境品种的cotangent束具有数值有效（NEF），或者更一般而言，当邻脑歧管接受有限的形态对具有NEF Cotangengent束的复杂射击歧管时。
We propose singular variants of the Singer-Hopf conjecture, formulated in terms of the Euler-Mather characteristic, intersection homology Euler characteristic and, resp., virtual Euler characteristic of a closed irreducible subvariety of an aspherical complex projective manifold. We prove the conjecture under the assumption that the cotangent bundle of the ambient variety is numerically effective (nef), or, more generally, when the ambient manifold admits a finite morphism to a complex projective manifold with a nef cotangent bundle.
