8/22/2023 0 Comments Calabi yau manifold![]() I.e.a projection map from a point off the manifold is always holomorphic, and is an embedding if it does not lie on a secant of the embedded manifold. If some questions don't make sense, sorry, hopefully they can be modified so that they do make sense.Īlthough there exist non projective complex manifolds, if a compact complex manifold of dimension n is projective, then it embeds holomorphically in CP^(2n+1), by the usual method of projecting it down from wherever you were able to embed it. In string theory do the vibrating strings interact with the Calabi-Yau manifold to change the Calabi-Yau manifold even if a little bit? What cool things "happen" when we allow for complex manifolds that don't happen for real manifolds? Is there a 6D Calabi-Yau manifold that could be considered most simple? How are 6D Calabi-Yau manifolds classified?ĭoes it make sense to take some 6D Calabi-Yau manifold and distort its shape a little and still keep it the "same" topologically?Ĭan we distort one 6D Calabi-Yau manifold into another?ĭoes it make sense to say that there is a minimum number of "flat" complex dimensions a typical 6D Calabi-Yau manifold can be embedded? Is there a finite number of slices of a 6D Calabi-Yau manifold that in principle could define that Calabi-Yau manifold? Mathematically what does it mean to take a "2D slice of a 6D Calabi-Yau manifold"? "2D slice of a 6D Calabi-Yau manifold", and other?
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