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In algebraic geometry, the problem of reso … In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4. an open problem in dimensions at least 4.
, 代数幾何学の特異点解消（とくいてんかいしょう、英: resolution of singularities）の問題とは、すべての代数多様体 V が特異点の解消を持つかどうか、つまり V に対して非特異代数多様体 W であって固有な双有理写像 W→V を持つものを見つけられるかどうかを問う問題である。標数0の体上の代数多様体については広中平祐によって1964年に肯定的に解決されている。しかし標数 p では4次元以上で未解決である。
, 在代數幾何學中，奇點解消問題探討代數簇是否有非奇異的模型（即：與之雙有理等價的非奇異代數簇）。在特徵為零的域上，廣中平祐已給出肯定答案，至於正特徵的域，四維以上的情形至今（2007年）未解。
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The lingering perception that the proof of resolution is very hard gradually diverged from reality. ... it is feasible to prove resolution in the last two weeks of a beginning algebraic geometry course.
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在代數幾何學中，奇點解消問題探討代數簇是否有非奇異的模型（即：與之雙有理等價的非奇異代數簇）。在特徵為零的域上，廣中平祐已給出肯定答案，至於正特徵的域，四維以上的情形至今（2007年）未解。
, In algebraic geometry, the problem of reso … In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V. For varieties over fields of characteristic 0 this was proved in Hironaka (1964), while for varieties over fields of characteristic p it is an open problem in dimensions at least 4. an open problem in dimensions at least 4.
, 代数幾何学の特異点解消（とくいてんかいしょう、英: resolution of singularities）の問題とは、すべての代数多様体 V が特異点の解消を持つかどうか、つまり V に対して非特異代数多様体 W であって固有な双有理写像 W→V を持つものを見つけられるかどうかを問う問題である。標数0の体上の代数多様体については広中平祐によって1964年に肯定的に解決されている。しかし標数 p では4次元以上で未解決である。
|
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Resolution of singularities
, 奇點解消
, 特異点解消
|
