论文标题
与Cotangent Bundle相关的非切片超人
Non-split supermanifolds associated with the cotangent bundle
论文作者
论文摘要
在这里，我研究了具有缩回拆分的超级男性$（m，ω）$的非切割超人的分类问题，其中$ω$是给定的复杂歧管$ m $ dimension $> 1 $的全态形式的捆绑。我提出了一个通用建筑，与任何$ d $ cluct的$（1,1）$ - 表格$ω$上的$ m $ $ m $ a $ m $ a $ m $，缩回$（m，ω）$，每当$ω$的dolbeault类是非零的，这是不分类的。特别是，这为任何标志歧管$ m \ ne \ ne \ mathbb {cp}^1 $提供了一个非空地的超级超人群家族。如果$ m $是不可约紧密的赫尔米尼亚对称空间的情况，我可以通过缩回$（m，ω）$进行完全分类的非切片超人质量分类。对于这些超男性，计算了带有切线中值的0和1-综合体。例如，我研究了Yu引入的$π$ -SMMETRIC SUPER-GRASSMANIAN。曼宁。
Here, I study the problem of classification of non-split supermanifolds having as retract the split supermanifold $(M,Ω)$, where $Ω$ is the sheaf of holomorphic forms on a given complex manifold $M$ of dimension $> 1$. I propose a general construction associating with any $d$-closed $(1,1)$-form $ω$ on $M$ a supermanifold with retract $(M,Ω)$ which is non-split whenever the Dolbeault class of $ω$ is non-zero. In particular, this gives a non-empty family of non-split supermanifolds for any flag manifold $M\ne \mathbb{CP}^1$. In the case where $M$ is an irreducible compact Hermitian symmetric space, I get a complete classification of non-split supermanifolds with retract $(M,Ω)$. For each of these supermanifolds, the 0- and 1-cohomology with values in the tangent sheaf are calculated. As an example, I study the $Π$-symmetric super-Grassmannians introduced by Yu. Manin.
