Optimal pinching for the holomorphic sectional curvature of Hitchin's metrics on Hirzebruch surfaces

The main result of this note is that, for each $n\in \{1,2,3,\ldots\}$, there exists a Hodge metric on the $n$-th Hirzebruch surface whose positive holomorphic sectional curvature is $\frac{1}{(1+2n)^2}$-pinched. The type of metric under consideration was first studied by Hitchin in this context. In...

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Hauptverfasser:	Alvarez, Angelynn, Chaturvedi, Ananya, Heier, Gordon
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Algebraic Geometry Mathematics - Complex Variables Mathematics - Differential Geometry
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