The Nakai conjecture is an unproven characterization of smooth algebraic varieties, proposed in 1961 by the Japanese mathematician Yoshikazu Nakai. It states that if V is a complex algebraic variety whose ring of differential operators is generated by the derivations it contains, then V must be a smooth variety.
Facts
StatementIf V is a complex algebraic variety whose ring of differential operators is generated by the derivations it contains, then V must be a smooth variety. 1 Proposed Year Progress Toward ResolutionThe Nakai conjecture is known to be true for algebraic curves. 1 Classification
Resolution Status Prize Status
Prize Status (category) Sources
1. Nakai Conjecture, Wikipedia
Introduction section
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
Introduction section, first sentence
In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961.
Main text, known cases paragraph
known to be true for algebraic curves
- Lead section
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