We prove the existence and uniqueness of Kähler–Einstein metrics on ℚ-Fano varieties with
log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional …

Full article: Open problems in pluripotential theory Skip to Main Content Taylor and Francis
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We survey the metric aspects of the Strominger–Yau–Zaslow conjecture on the existence of
special Lagrangian fibrations on Calabi–Yau manifolds near the large complex structure …

In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …

Let X be any Q Q-Fano variety and Aut (X) _0 Aut (X) 0 be the identity component of the
automorphism group of X. Let GG be a connected reductive subgroup of Aut (X) _0 Aut (X) 0 …

Let L be an ample line bundle on a (geometrically reduced) projective variety X over any
complete valued field. Our main result describes the leading asymptotics of the determinant …

We prove the following result: if a\,\,\,\, Q\,\,\,\,\, Q-Fano variety is uniformly K-stable, then it
admits a Kähler–Einstein metric. This proves the uniform version of Yau–Tian–Donaldson …

We prove that the non-Kähler locus of a nef and big class on a compact complex manifold
bimeromorphic to a Kähler manifold equals its null locus. In particular this gives an analytic …

For a large class of maximally degenerate families of Calabi–Yau hypersurfaces of complex
projective space, we study non-Archimedean and tropical Monge–Ampère equations, taking …

We show that on a Kähler manifold whether the $ J $-flow converges or not is independent
of the chosen background metric in its Kähler class. On toric manifolds we give a numerical …