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Results tagged with calabi-yau
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user 23917
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.
12
votes
For which Calabi-Yau threefolds is SYZ conjecture known to hold?
Let me go from the weakest to strongest sense in which the conjecture should
be true.
First, at the purely topological level, it is true for any Calabi-Yau variety
with a toric degeneration whose dua …
12
votes
Accepted
Hodge Numbers and Leray Spectral Sequence
I don't think I defined the Hodge numbers in this way. Rather, the argument in Section 1 shows that the Hodge numbers agree with the dimensions of
the terms in the $E_2$ page of the Leray spectral seq …
- 985
9
votes
What information is required for SYZ mirror symmetry?
I'll fill in a few details here; more can be found in the references that Daniel gave.
Suppose first that $f:X\rightarrow B$ is a special Lagrangian $T^n$ fibration with only
smooth fibres. If we jus …
- 985
8
votes
The moduli space of special Lagrangian submanifolds
Both the elliptic curve and K3 case can be calculated explicitly, the first more than the second.
First let's recall how the structures arise. We have the 2-form $\omega$ and
the $n$-form $\Im \Omeg …
- 985
6
votes
Accepted
Factoriality of one-nodal Calabi-Yau threefolds
Let $X$ be a Calabi-Yau three-fold with only ordinary double points. One can always find a small resolution $Y\rightarrow X$ where $Y$ is a (not necessarily Kaehler) complex manifold. Let $C_1,\ldots, …
- 985
4
votes
A question on the topological change of dualizing a SLAG fibration.
The crucial point for the second question is the following. In arbitrary dimension, it is not true that $\pi^{-1}(B_0)$ and $\pi^{-1}(B_0)^{\vee}$ are homeomorphic as fibre bundles. This is essentiall …
- 985