On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature (with an appendix by Yuchen Liu)

Abstract

Using $\delta$-invariants and Newton--Okounkov bodies, we derive the optimal volume upper bound for Kähler manifolds with positive Ricci curvature, from which we get a new characterization of the complex projective space.

Final version, to appear in Int. Math. Res. Not. IMRN