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The sign of scalar curvature on Kähler blowups
Published 20 May 2024 in math.DG and math.AG | (2405.12189v1)
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.
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