Geodesic
Strict positivity of Kähler–Einstein currents
Forum of Mathematics, Sigma, Tome 12 (2024)

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Kähler–Einstein currents, also known as singular Kähler–Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular compact Kähler spaces X and their two defining properties are the following: They are genuine Kähler–Einstein metrics on $X_{\mathrm {reg}}$, and they admit local bounded potentials near the singularities of X. In this note, we show that these currents dominate a Kähler form near the singular locus, when either X admits a global smoothing, or when X has isolated smoothable singularities. Our results apply to klt pairs and allow us to show that if X is any compact Kähler space of dimension three with log terminal singularities, then any singular Kähler–Einstein metric of nonpositive curvature dominates a Kähler form. 
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     author = {Vincent Guedj and Henri Guenancia and Ahmed Zeriahi},
     title = {Strict positivity of {K\"ahler{\textendash}Einstein} currents},
     journal = {Forum of Mathematics, Sigma},
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     year = {2024},
     doi = {10.1017/fms.2024.54},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2024.54/}
}
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Vincent Guedj; Henri Guenancia; Ahmed Zeriahi. Strict positivity of Kähler–Einstein currents. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.54

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