Zariski's Main Theorem: Power Series Form
A formal power series version of Zariski's main theorem says that if x is a point of a normal variety then the completion of the local ring at x is a normal integral domain (Mumford 1999, III.9).
Read more about this topic: Zariski's Main Theorem
Famous quotes containing the words main, power, series and/or form:
“I do not deny that there may be other well-founded causes for the hatred which various classes feel toward politicians, but the main one seems to me that politicians are symbols of the fact that every class must take every other class into account.”
—José Ortega Y Gasset (1883–1955)
“Despots play their part in the works of thinkers. Fettered words are terrible words. The writer doubles and trebles the power of his writing when a ruler imposes silence on the people. Something emerges from that enforced silence, a mysterious fullness which filters through and becomes steely in the thought. Repression in history leads to conciseness in the historian, and the rocklike hardness of much celebrated prose is due to the tempering of the tyrant.”
—Victor Hugo (1802–1885)
“Personality is an unbroken series of successful gestures.”
—F. Scott Fitzgerald (1896–1940)
“Is civilization only a higher form of idolatry, that man should bow down to a flesh-brush, to flannels, to baths, diet, exercise, and air?”
—Mary Baker Eddy (1821–1910)