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In algebraic geometry, a weighted projective space P(''a''0,...,''a''''n'') is the projective variety Proj(''k''()) associated to the graded ring ''k''() where the variable ''x''''k'' has degree ''a''''k''. ==Properties== *If ''d'' is a positive integer then P(''a''0,''a''1,...,''a''''n'') is isomorphic to P(''a''0,''da''1,...,''da''''n'') (with no factor of ''d'' in front of ''a''0), so one can without loss of generality assume that any set of ''n'' variables ''a'' have no common factor greater than 1. In this case the weighted projective space is called well-formed. *The only singularities of weighted projective space are cyclic quotient singularities. *A weighted projective space is a Fano variety and a toric variety. *The weighted projective space P(''a''0,''a''1,...,''a''''n'') is isomorphic to the quotient of projective space by the group that is the product of the groups of roots of unity of orders ''a''0,''a''1,...,''a''''n'' acting diagonally. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Weighted projective space」の詳細全文を読む スポンサード リンク
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