The volume of Kähler–Einstein Fano varieties and convex bodies
The volume of Kähler–Einstein Fano varieties and convex bodies
Abstract We show that the complex projective space <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>ℙ</m:mi><m:mi>n</m:mi></m:msup></m:math> ${\mathbb{P}^{n}}$ has maximal degree (volume) among all n -dimensional Kähler–Einstein Fano manifolds admitting a non-trivial holomorphic <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msup><m:mi>ℂ</m:mi><m:mo>*</m:mo></m:msup></m:math> ${\mathbb{C}^{*}}$ -action with a finite number of fixed points. The toric version of this result, translated to the realm of convex geometry, …