Explicit Birational Geometry of 3-Folds: Singularities of linear systems and 3-fold birational geometry

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IMPANGA lecture notes on log canonical thresholds (2011, background): “This is a point of view due to Corti [Cor] on the classical approach to the non-rationality of a quartic threefold of Iskovskikh and Manin [IM].”
On multiplicities of graded sequences of ideals (2002, methodology): “In the case of one ideal, this appeared in [FEM], generalizing the corresponding inequality due to Corti, for the case of surfaces (see [Co]).”
Hyperelliptic and trigonal Fano threefolds (2004, background): “The birational geometry of such 3-folds was studied in [22], [54], [37], [16], [28], [63], [64], [102], [58].”
F-Thresholds, tight closure, integral closure, and multiplicity bounds (2007, background): “The corresponding inequality between the multiplicity and the log canonical threshold of a was proved in [dFEM], and plays a key role in proving that for small values of n, no smooth hypersurface of degree n in P is rational (see [Cor] and [?]).”
Birational Geometry of 3-fold Mori Fibre Spaces (2003, background): “A few general criteria for birational rigidity have been known for quite some time, see [IP96], [Cor00].”
Multiplicities and log canonical threshold (2002, background): “In the special case when Supp(F ) has exactly two smooth branches meeting transversally at p, Theorem 2.4 implies an earlier result of Corti [Co].”