复环面流形的Todd亏格
Todd genera of complex torus manifolds
摘要：
本文证明了当$X$的自同构群包含一个紧致$n$维环面$\Tn$作为子群时，具有零奇次上同调的紧致复流形$X$的Todd亏格为1.这意味着，如果一个拟流形允许一个不变的复结构，那么它是等变同胚到一个紧光滑环面簇，这给出了一个否定的答案由Buchstaber-Panov提出的问题。
英文摘要：
In this paper, we prove that the Todd genus of a compact complex manifold $X$ of complex dimension $n$ with vanishing odd degree cohomology is one if the automorphism group of $X$ contains a compact $n$-dimensional torus $\Tn$ as a subgroup. This implies that if a quasitoric manifold admits an invariant complex structure, then it is equivariantly homeomorphic to a compact smooth toric variety, which gives a negative answer to a problem posed by Buchstaber-Panov.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
