论文标题
Inoue表面，Kodaira表面及其爆炸的Yamabe不变性
The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups
论文作者
论文摘要
引入Seiberg-Witten理论后不久，LeBrun表明，紧凑型Kähler表面的Yamabe不变的迹象取决于其Kodaira尺寸。在本文中，我们表明勒布朗的定理不再是非kähler表面的事实。特别是，我们表明，Inoue表面的Yamabe不变性及其爆炸都是零。我们还借此机会记录了一个证据，表明Kodaira表面的Yamabe不变性及其爆炸都是零，如Lebrun先前所示。
Shortly after the introduction of Seiberg-Witten theory, LeBrun showed that the sign of the Yamabe invariant of a compact Kähler surface is determined by its Kodaira dimension. In this paper, we show that LeBrun's Theorem is no longer true for non-Kähler surfaces. In particular, we show that the Yamabe invariants of Inoue surfaces and their blowups are all zero. We also take this opportunity to record a proof that the Yamabe invariants of Kodaira surfaces and their blowups are all zero, as previously indicated by LeBrun.
