Resolution of singularities for 3-folds in positive characteristic

By Steven Dale Cutkosky. 2006

117 citations recorded by the source corpus.

A concise, complete proof of resolution of singularities of 3-folds in positive characteristic $>5$ is given. Abhyankar first proved this theorem in 1966.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d731b898810007efb012f5860de2fa59124945dd

How researchers see this paper

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In Algebra and Number Theory

1. Ana Bravo
2. C. Birkar
3. Orlando Villamayor
4. Christopher D. Hacon
5. J. Witaszek
6. J. Waldron
7. Mihnea Cristian Popa
8. C. Schnell

In Geometry and Topology

1. C. Birkar
2. Christopher D. Hacon
3. Ana Bravo
4. J. Waldron
5. Orlando Villamayor
6. J. Witaszek
7. O. Fujino
8. Chi Li

In Mathematical Physics

1. C. Birkar
2. Christopher D. Hacon
3. Ana Bravo
4. Orlando Villamayor
5. J. Witaszek
6. J. Waldron
7. J. McKernan
8. Herwig Hauser

Citations in the corpus

• Singularities in positive characteristic, stratification and simplification of the singular locus (2008, background): “es ([6], [11], [16], [26], [29], [30], [34]). There are some results on low dimensional varieties over arbitrary fields by Abhyankar, and more recently by some other authors (see also [7], [8]), [9]), [10]) but the general question of resolution remains open. Another important contribution is de Jong”
• Resolution of singularities of arithmetical threefolds (2014, unknown): “In dimension three, some partial results do exist for algebraic varieties over an algebraically closed field k of positive characteristic p ≥ 7 [5][32].”
• Existence of Mori fibre spaces for 3-folds in char $p$ (2014, background): “This follows from [11] when k has characteristic”
• RESOLUTION OF SINGULARITIES OF THREEFOLDS IN POSITIVE CHARACTERISTIC II (2008, unknown): “Abhyankar’s techniques have been greatly simplified in [ 17 ] under the same assumption on k. Although several written programs have appeared in the recent years to prove resolution of singularities [30] [28] or the weaker local uniformization theorem [43] over a perfect ground field, none has been ”
• On the rationality of Kawamata log terminal singularities in positive characteristic (2017, background): “If X is of dimension at most three, then a log resolution of ( X, D ) always exists (see [Lip78, Cut09, CP08, CP09]).”