Perron Transforms

REFERENCES

• Abhyankar , S. ( 1956 ). Local uniformization on algebraic surfaces over ground fields of characteristic p ≠ 0 . Annals of Mathematics 63 : 491 – 526 .
   Web of Science ®Google Scholar
• Abhyankar , S. ( 1960 ). Ramification theoretic methods in algebraic geometry . Bulletin of the American Mathematical Society 4 : 250 – 252 .
   Google Scholar
• Abhyankar , S. ( 1998 ). Resolution of Singularities of Embedded Algebraic Surfaces. , 2nd ed. New York , Berlin, Heidelberg : Springer Verlag .
   Google Scholar
• Cossart , V. , Piltant , O. ( 2008 ). Resolution of singularities of threefolds in positive characteristic I . J. Algebra 320 : 1051 – 1082 .
   Web of Science ®Google Scholar
• Cossart , V. , Piltant , O. ( 2009 ). Resolution of singularities of threefolds in positive characteristic II . J. Algebra 321 : 1836 – 1976 .
   Web of Science ®Google Scholar
• Cutkosky , S. D. ( 1999 ). Local monomialization and factorizations of morphisms . Astérisque 260 .
   Google Scholar
• Cutkosky , S. D. , ElHitti , S. ( 2010 ). Formal prime ideals of infinite value and their algebraic resolution . Annales de la Faculté des Sciences de Toulouse Sér. 6 , 19 : 635 – 649 .
   Google Scholar
• Cutkosky , S. D. , Ghezzi , L. ( 2005 ). Completions of Valuation Rings, Recent Progress in Arithmetic and Algebraic Geometry . Contemporary Mathematics , Vol. 386 . Providence , RI : American Mathematical Society , pp. 13 – 34 .
   Google Scholar
• Perron , O. ( 1906 ). Grundlagen fur eine Theorie des Jacobischen Kettenbruchalgorithmen . Leipzig : Habilitationsschrift .
   Google Scholar
• Spivakovsky , M. ( 1990 ). Sandwiched singularities and desingularization of surfaces by normalized Nash transforms . Annals of Mathematics 131 : 441 – 491 .
   Google Scholar
• Spivakovsky , M. ( 1990 ). Valuations in function fields of surfaces . American Journal of Mathematics 112 : 107 – 156 .
   Web of Science ®Google Scholar
• Teissier , B. ( 2003 ). Valuations, Deformations and Toric Geometry . Fields institute communications , Vol. 33 . Providence , RI : American Mathematical Society , pp. 361 – 459 .
   Google Scholar
• Temkin , M. ( 2013 ). Inseparable local uniformization . Journal of Algebra 373 : 65 – 119 .
   Web of Science ®Google Scholar
• Zariski , O. ( 1939 ). The reduction of singularities of an algebraic surface . Annals of Mathematics 40 : 639 – 689 .
   Google Scholar
• Zariski , O. ( 1940 ). Local uniformization of algebraic varieties . Annals of Mathematics 41 : 852 – 896 .
   Google Scholar
• Zariski , O. , Samuel , P. ( 1960 ). Commutative Algebra . Vol. 2 . Princeton : Van Nostrand .
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar