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Results tagged with calabi-yau
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user 38468
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.
7
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Resolving nodes of a quintic CY 3-fold
I assume that you mean $x_1=x_2=0$ in your description of the divisors. I believe that you only really get two different resolutions, but yes, they are both projective varieties. Hodge numbers of bira …
- 5,186
35
votes
1
answer
1k
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What is the meaning of $(h^{11},h^{21})\to (h^{11}-240,h^{21}+240)$ in Calabi-Yau threefolds?
By browsing through the Hodge data of known Calabi-Yau threefolds, I stumbled upon an observation that frequently enough a pair of Hodge numbers $(h^{11},h^{21})$ comes together with the pair $ (h^{1 …
CommunityBot
- 1
8
votes
2
answers
461
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Necessary condition on Calabi-Yau manfiold to be a hypersurface in a Fano manifold
Let $X$ be a smooth projective Calabi-Yau threefold. Are there any known obstructions to it
being a member of a base-point-free linear system in a nef-Fano fourfold?
What, in anything, is known rega …
- 38k
3
votes
Why is the mirror of rigid Calabi-Yau threefold singularity theory?
There is a toric complete intersection example, rather ad hoc, in arXiv:alg-geom/9402002.
This particular example is related to the situation when a decomposition
of anticanonical class on toric Fano …
- 5,186