Lectures on resolution of singularities

By J. Kollár. 2007

481 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/c351e602041d95d0d843a3333bae83967b2541c2

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1. Chi Li
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Citations in the corpus

• Functorial desingularization over Q: boundaries and the embedded case (2009, background): “, if we consider a blow up of schemes f: X′ → X as a B-blow up of B-schemes (X′,E′) → (X,∅), then the center is almost always determined by the B-blow up, and similarly for the blow up sequences from [Kol07]. The only small redundancy with B-blow ups was described in Remark 2.2.12(i), and even that ”
• Differential forms on log canonical spaces (2010, background): “resolution of (X,D) if the following property holds in addition. (2.12.4) The rational map π−1 is a well-defined isomorphism over the open set(X,D)reg. Fact 2.13 (Hironaka’stheorem on resolutions, cf. [Kol07]). Log resolutions and strong log resolutions exist. Remark 2.14. Let (X,D)be a pair, and π: ”
• Resolution of singularities for 3-folds in positive characteristic (2006, methodology): “Several simplifications of Hironaka’s proof of characteristic zero resolution have appeared, making the proof quite accessible now, including Abramovich and de Jong [AJo], Bierstone and Milman [BrM], Bogomolov and Pantev [BP], Bravo, Encinas and Villamayor [BEV], Encinas and Hauser [EH], Encinas and”
• The Uniform Version of Yau–Tian–Donaldson Conjecture for Singular Fano Varieties (2019, background): “There is always such a resolution which is obtained by embedding X into an smooth ambient spaces and taking the strict transform of X under a sequence of blowups along smooth centers (see [43]).”
• Functorial desingularization of quasi-excellent schemes in characteristic zero: the nonembedded case (2009, methodology): “m Y f→BlV (X) is fixed. The reason for this change is that we will study functoriality, and the choice of V increases canonicity of constructions, see, for example, §2.2.6. Following the convention of [Kol] we call a blow up Bl∅(X)f→X empty or trivial blow up. This is the only blow up we will sometim”
• Representation growth and rational singularities of the moduli space of local systems (2013, background): “A more recent overview can be found in [Kol].”
• Functoriality in Resolution of Singularities (2007, methodology): “Our proof shows that the association of a resolution sequence to a marked ideal is also functorial with respect to field extensions and to closed embeddings ι : M ↪→ M ′ in the case that d = 1 (as in [W], [Ko]), but we do not explicitly discuss these issues.”