English

Kodaira Dimension and the Yamabe Problem, II

Differential Geometry 2021-12-15 v2 Algebraic Geometry Complex Variables

Abstract

For compact complex surfaces (M^4, J) of Kaehler type, it was previously shown that the sign of the Yamabe invariant Y(M) only depends on the Kodaira dimension Kod (M, J). In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we give a simplified proof of a result that explains why the exclusion of class VII is essential here.

Cite

@article{arxiv.2106.14333,
  title  = {Kodaira Dimension and the Yamabe Problem, II},
  author = {Michael Albanese and Claude LeBrun},
  journal= {arXiv preprint arXiv:2106.14333},
  year   = {2021}
}

Comments

25 pages, LaTeX2e

R2 v1 2026-06-24T03:38:50.913Z