2020/05/19 by Michael Albanese, Albanese, Michael · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2005.09494
openalex publication_date 2020/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Shortly after the introduction of Seiberg-Witten theory, LeBrun showed that\nthe sign of the Yamabe invariant of a compact K "ahler surface is determined by\nits Kodaira dimension. In this paper, we show that LeBrun's Theorem is no\nlonger true for non-K "ahler surfaces. In particular, we show that the Yamabe\ninvariants of Inoue surfaces and their blowups are all zero. We also take this\nopportunity to record a proof that the Yamabe invariants of Kodaira surfaces\nand their blowups are all zero, as previously indicated by LeBrun.\n