Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry

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We prove a general result about the geometry of holomorphic line bundles over Kähler manifolds.

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Regularity of Kähler–Ricci flows on Fano manifolds (2013, unknown): “Inspired by [42], [41] and [19], we have the following extension of the partial Cestimates to Kähler–Ricci flows.”
Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II (2015, methodology): “1 is similar to the one we used in the proof of Theorem 2 in [16].”
Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, methodology): “When the metrics along the sequence are Kähler-Einstein, DonaldsonSun [17] showed that the metric singular set of Y is the same as the complex analytic singular set of the corresponding projective variety (see also Corollary 4.”
K‐Stability and Kähler‐Einstein Metrics (2012, unknown): “As indicated in [47] and verified in [24] for smooth Kähler-Einstein metrics (also see [30]), by the arguments in the proof of the partial C -estimate, we can prove the following regularity for M1: THEOREM 5.”
Space of Ricci Flows I (2009, methodology): “It follows from the argument in [49] that the constant section 1 of the trivial bundle over Ŷ can be “pulled back” as a non-vanishing holomorphic section of L over B(x, 10), up to a finite lifting of power of L.”