Equivariant resolution of singularities in characteristic 0
Dan Abramovich,Jianhua Wang +1 more
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In this paper, a new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided, assuming that we know how to resolve singularities without group action.Abstract:
A new proof of equivariant resolution of singularities under a finite group action in characteristic 0 is provided. We assume we know how to resolve singularities without group action. We first prove equivariant resolution of toroidal singularities. Then we reduce the general case to the toroidal case.read more
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Torification and Factorization of Birational Maps
TL;DR: In this article, the weak factorization conjecture for birational maps in characteristic zero was shown to hold for algebraic and analytic spaces, and the same holds for analytic spaces as well.
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Torification and factorization of birational maps
TL;DR: In this paper, the weak factorization conjecture for birational maps in characteristic zero was shown to hold for algebraic and analytic spaces, and the same holds for analytic spaces as well.
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Finite Subgroups of the Plane Cremona Group
TL;DR: In this paper, the classic and modern results on classification of conjugacy classes of finite subgroups of the group of birational automorphisms of the complex projective plane are complete.
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The Hironaka theorem on resolution of singularities (Or: A proof we always wanted to understand)
TL;DR: In this article, a handyman's manual for learning how to resolve the singularities of algebraic varieties defined over a field of characteristic zero by sequences of blowups is presented. But it does not address the problem of how to prove resolution of singularities in characteristic zero.
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Strong resolution of singularities in characteristic zero
Santiago Encinas,Herwig Hauser +1 more
TL;DR: In this article, the authors present a concise proof for the existence and construction of a strong resolution of excellent schemes of finite type over a field of characteristic zero, based on earlier work of Encinas-Villamayor, Bierstone-Milman and others.
References
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Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: II
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Constructiveness of Hironaka's resolution
TL;DR: Gauthier-Villars as discussed by the authors implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions).
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Smoothness, Semistability, and Toroidal Geometry
Dan Abramovich,Johan de Jong +1 more
TL;DR: In this article, Bogomolov and Pantev gave a weak version of Hironaka's well known theorem on resolution of singularities, which is based on semistable reduction for curves and toric geometry.
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Weak Hironaka theorem
Fedor Bogomolov,Tony Pantev +1 more
TL;DR: Abrahamovich and de Jong as discussed by the authors gave a simple proof of the following theorem: a normal projective variety over an algebraically closed field can be shown to be a proper closed subvariety of the original projective manifold.