Nakai conjecture

Nakai conjecture: 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 variety V with coordinate ring R: if the derivations of R are a free module over R, then V is smooth.

Sources

Google Scholar results for: nakai conjecture

Nakai's Conjecture for Varieties Smoothed by Normalization,William N. Traves, Proceedings of the American Mathematical Society, Vol. 127, No. 8 (Aug., 1999), pp. 2245-2248

Categories:
Algebraic geometry
Singularity theory
Conjectures

Игры ⚽ Поможем написать реферат

Nakai — may refer to: Nakai Misl, a principality of the Punjab Region Nakai (中井, hiragana: なかい) can be a Japanese surname Nakai (Japanese vocation) People named Nakai Nakai Chikuzan, a politician Kazuya Nakai, an actor Kiichi Nakai, an actor Masahiro… … Wikipedia
List of mathematics articles (N) — NOTOC N N body problem N category N category number N connected space N dimensional sequential move puzzles N dimensional space N huge cardinal N jet N Mahlo cardinal N monoid N player game N set N skeleton N sphere N! conjecture Nabla symbol… … Wikipedia
Magnesium diboride — Identifiers CAS number … Wikipedia
JESUS — (d. 30 C.E.), whom Christianity sees as its founder and object of faith, was a Jew who lived toward the end of the Second Commonwealth period. The martyrdom of his brother James is narrated by Josephus (Ant. 20:200–3), but the passage in the same … Encyclopedia of Judaism

Academic Dictionaries and Encyclopedias