The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups

Michael Albanese

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arXiv · 2005.09494

The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups

Michael Albanese

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Abstract

Shortly after the introduction of Seiberg-Witten theory, LeBrun showed that the sign of the Yamabe invariant of a compact K\"ahler surface is determined by its Kodaira dimension. In this paper, we show that LeBrun's Theorem is no longer true for non-K\"ahler 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.

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Michael Albanese. 2020-05-19. The Yamabe invariants of Inoue surfaces, Kodaira surfaces, and their blowups. https://arxiv.org/abs/2005.09494

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