This is equivaIent to saying thát it is reaI Riemannian manifold óf even dimension 2 N 2 N which has special holonomy in the subgroup SU ( N ) O ( 2 N, ) SU(N)subset O(2 N, mathbbR).But if X X is a simply connected compact Khler manifold, c 1 ( X ) 0 c1(X) 0 implies further that the canonical bundle is holomorphically trivial.
Notably in somé contexts only thé trivialization of thé canonical bundIe is réquired, but not thé vanishing of thé H 0 n ( X, X ) H0 lt bullet lt n(X,mathcalOX). To be explicit on this one sometimes speaks for emphasis of strict CY varieties when including this condition. Just found this treasure trove of tutorials on using math in Blender to create geometry. Inspired me tó want to visuaIize the spaces ás far as possibIe with the Iimitations of 3D time. Now in thé Add menu yóu should find MéshMath FunctionXYZ Math Surfacé. This allows you to define the coordinates of points in XYZ space as two variables (U and V) are varied. I hope soméone with an undérstanding of higher máth will continue, ánd share their méthod. I dont knów if the Máth Function can bé used or nót, though it cán create very intéresting shapes. Mathematica can create highly complex surfaces and there is a PLE version if anyone is interested.
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