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Register a new userA study in the resolution of singularity on a field with characteristic ≠ 2
دراسة في حل الشذوذية على حقل مميزه ≠ 2
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تعد الشذوذات بشكل عام من الموضوعات المهمة في الهندسة الجبرية و الرياضـيات التطبيقيـة. و منها البسيطة أو الشذوذات من النمط ADE التي لفتت الانتباه لكونها ظهـرت بـشكل منفـصل فـي مجالات مختلفة من التطبيقات العلمية و تعود التسمية لثلاثة أشكال مرمزة بـالأحرف A و D و E تعبـر عن أنماط من زمر لي، و قد طرح أرنولد Arnold العلاقات المعبرة عنها بشكل صريح، و هناك كثيرون ممن قدموا دراسات مهمة في الموضوع مثل M. Roczen الذي قدم الحل القانوني لها فـي البعـد 3 على حقل مميزه لا يساوي 2 ،و يقصد بالحل إيجاد متنوعة مكافئة لهذه المتنوعة تكون غير شاذة، أمـا الحل القانوني فيضيف وصفاً إلى المحل الاستثنائي.
Singularities in general are considered to be one of the important issues in algebraic geometry and applied mathematics, among them the ADE or simple singularities which drew attention since they have appeared separately in various areas of scientific applications. The name comes from three graphs characterized by letters A, D and E denoting types of Lie groups. Arnold stated them in a direct manner. Many people gave studies about the subject like Roczen.M who presented the canonical resolution in dimension 3 and Char ≠ 2. giving an equivalent non-singular variety is what meant by resolution, Canonical resolution adds a description of the exceptional loci.
References used
Alwadi. Y. (2002). "Simple and Semiquasihomogeneous Singularities" Damascus University of BASIC SCIENCES Vol. 18, No 1
Greuel, G. M., Kroning, H. (1990). "Simple singularities in positive characteristic" Math. Z. 203, 339-354
Hartshorne. R. (1977). "Algebraic Geometry" Springer Verlag
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