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July 09, 2006
"It was a six hour bus ride with a lot of stops. May I have some water please?" "Sorry, my parents aren't home. But you could use the hose out front." "Delightful!"
Trying to make sense of Dan Simmon's Ilium-Olympos duology, I checked out the Wikipedia page on Calabi-Yau manifolds, which has to be the most abstruse entry on the entire site. I mean, is this even English?
A Calabi-Yau manifold is a Kähler manifold with a vanishing first Chern class. A Calabi-Yau manifold of complex dimension n is also called a Calabi-Yau n-fold. The mathematician Eugenio Calabi conjectured in 1957 that all such manifolds admit a Ricci-flat metric (one in each Kähler class), and this conjecture was proved by Shing-Tung Yau in 1977 and became Yau's theorem. Consequently, a Calabi-Yau manifold can also be defined as a compact Ricci-flat Kähler manifold.
Equivalently one may define a Calabi-Yau n-fold as a manifold with an SU(n) holonomy. Yet another equivalent condition is that the manifold admit a global nowhere vanishing holomorphic (n,0)-form.
The first Chern class vanishes if and only if the canonical bundle is trivial, which in turn is the case if and only if the canonical class is the zero class. While the Chern class fails to be well-defined for singular Calabi-Yau's, the canonical bundle and canonical class may still be defined and so may be used to extend to definition of a smooth Calabi-Yau manifold to a possibly singular Calabi-Yau variety.
The Talk page for the Calabi-Yau Wikipedia entry is hilarious. Regular people complain that not only does the entry not make any sense to the layman, but neither do any of the other entries it links to. Physicists, in turn, do their best to try to explain this stuff simply but can't do better than the following, which makes no more sense to me than the excerpt above:
A Calabi-Yau manifold is a particular type of Kähler manifold, which is a manifold which carries a complex structure and a Hermitian structure which are compatible in each other in a technical way. For a Kähler manifold to be Calabi-Yau manifold, its curvature form must be an exact differential, which also implies that the trace of its curvature form vanishes, according to a famous result by Calabi and Yau.
Supposedly Apple's got a new logic board available for MacBook Pros (again I wonder, should it be MacBooks Pro?).
Jack Abramoff visited the White House more often than they had previously admitted. via
The first set of documents released to Judicial Watch on May 10 indicated that Abramoff only made two visits to the White House on March 6, 2001 and January 20, 2004. The new documents show an additional seven data entries concerning Abramoff appointments on the following dates: March 1, 2001; March 6, 2001; April 20, 2001; May 9, 2001; May 17, 2001; December 7, 2001; and December 10, 2001. According to the cover letter accompanying the documents, “The…data reflect appointments involving Jack Abramoff, but do not necessarily reflect actual visits to the White House Complex.”
Ice spoon: its time has come
Bacon cereal: its time will never come.
Posted by Jon Rubin at July 9, 2006 07:53 PM
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