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Results tagged with calabi-yau
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user 38823
Calabi-Yau manifolds are higher dimensional generalizations of elliptic curves and K3 surfaces. They can be defined as the compact complex Kähler manifolds with trivial canonical bundle, and play a central role in mirror symmetry. This tag can also be used for Calabi-Yau algebras and categories. These algebraic notions are inspired by the properties of the derived categories of coherent sheaves on Calabi-Yau manifolds.
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Betti numbers of threefolds with trivial canonical class
I am interested in a simply-connected compact complex manifold $M$ of dimension three with trivial canonical class.
Note that if it is K"ahler, then it is a Calabi-Yau threefold.
Its independent Bett …
- 1,841
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Minimal Betti numbers of simply-connected threefolds with trivial canonical class
By a threefold, I mean a compact complex manifold of dimension three.
For a simply-connected threefold with trivial canonical class, its Betti numbers satisfy:
$$b_2 \ge 0, b_3 \ge 2.$$
I am wondering …
- 1,841
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Smallest Hodge numbers of Calabi-Yau threefolds ever found
By a Calabi-Yau threefold, I mean a simply-connected smooth compact K"ahler threefold with trivial canonical class.
It has two independent Hodge numbers $h^{1,1}$ and $h^{1,2}$.
What is the smallest …
- 1,841
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Mirror symmetry for K3 fibered Calabi-Yau threefolds
By a K3 fibered Calabi-Yau threefold, I mean a smooth projective threefold $X$ with trivial canonical class and
$h^{1,0}(X) =h^{2,0}(X) = 0$ that has a fibration $X \rightarrow \mathbb P^1$ whose gen …
- 426
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Examples or references for this claim about elliptic Calabi-Yau threefolds
In this article (page 2) , the authors say:
"it is expected, based on known examples, that Calabi–Yau threefolds of large Picard
rank are always elliptically fibered, perhaps after flopping a finite n …
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