Nakai Conjecture
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Nakai conjecture states that if V is a complex algebraic variety, such that its ring of differential operators is generated by the derivations it contains, then V is a smooth variety. This is the conjectural converse to a result of Alexander Grothendieck. It is known to be true for algebraic curves. The conjecture was proposed by the Japanese mathematician Yoshikazu Nakai. A consequence would be the Zariski-Lipman conjecture, for a complex affine v...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Nakai conjecture states that if V is a complex algebraic variety, such that its ring of differential operators is generated by the derivations it contains, then V is a smooth variety. This is the conjectural converse to a result of Alexander Grothendieck. It is known to be true for algebraic curves. The conjecture was proposed by the Japanese mathematician Yoshikazu Nakai. A consequence would be the Zariski-Lipman conjecture, for a complex affine variety V with coordinate ring R: if the derivations of R are a free module over R, then V is smooth.
