Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces

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Weighted Projective Embeddings, Stability of Orbifolds, and Constant Scarla Curvature Kär Metrics (2009, background): “ the corresponding Bergman kernel turns out not to be relevant to constant scalar curvature orbifold Kahler metrics. We learnt about the related alternative embedding (2.10) from Dan Abramovich; see [AH]. The idea of using weighted projective embeddings certainly goes back further to Miles Reid; see”
The Calabi conjecture and K-stability (2010, methodology): “ proved that the stable varieties admitting semi-log-canonical singularities also forms projective moduli as well by using LMMP-like method, not relying on the GIT theory (cf. e. g. [KSB88], [Ale94], [AH09], [Kol10]). Along the development of that generalization, a fundamental observation was that s”
Topological methods in algebraic geometry (2015, background): “moduli space (a phenomenon similar to the one which was observed in several papers, as [10,11, 16, 43]).”
Existence of log canonical closures (2011, background): “To verify that J is nef over U , we first remark that by [Kawamata10, 1(4)], the Q-line bundle J computed from X ′ → Y commutes with any pull back in the sense of [Kollár07, 8.4.9(3)].”
ACC for log canonical thresholds (2012, background): “More recently (1.1) was proved for complete intersections, [10], and even when X belongs to a bounded family, [11].”