自相交稳定广义复结构
Self-crossing stable generalized complex structures
AI总结：
本文将稳定广义复结构推广至允许反典范截面具有法向自相交奇异性，证明了四维情形下的连通和与光滑化操作，从而构造出大量稳定的广义复流形族。
摘要：
我们将（光滑）稳定广义复结构的概念推广至允许反典范截面具有法向自相交奇异性。这种弱化不仅为高维情形提供了诸多自然实例，也为四维光滑情形提供了新视角。我们证明，在四维中这些结构存在自然的连通和运算，以及一种将自相交稳定广义复结构转化为同一流形上光滑稳定广义复结构的光滑化操作。这使我们能够构造大量稳定的广义复流形族。
英文摘要：
We extend the notion of (smooth) stable generalized complex structures to allow for an anticanonical section with normal self-crossing singularities. This weakening not only allows for a number of natural examples in higher dimensions but also sheds some light into the smooth case in dimension four. We show that in four dimensions there is a natural connected sum operation for these structures as well as a smoothing operation which changes a self-crossing stable generalized complex structure into a smooth stable generalized complex structure on the same manifold. This allows us to construct large families of stable generalized complex manifolds.
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