1. The sign of scalar curvature on K\'ahler blowups
- Author
-
Brown, Garrett M.
- Subjects
Mathematics - Differential Geometry ,Mathematics - Algebraic Geometry - Abstract
We show that if $(M,\omega)$ is a compact K\"ahler manifold with positive/negative scalar curvature, then the blowup of $M$ at any point also furnishes a positive/negative scalar curvature K\"ahler metric in classes which make the exceptional divisor small. In the case of K\"ahler surfaces with positive scalar curvature, this extends a result of N. Hitchin to surfaces and answers a conjecture of C. LeBrun in the affirmative, as a result completing the classification of such surfaces., Comment: 21 pages, no figures, all comments are welcome
- Published
- 2024