Questions tagged [calabi-yau]
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.
62 questions with no upvoted or accepted answers
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Weil Petersson metric on moduli space of Calabi Yau manifolds
Let $f:(X,D)\to Y$ be a holomorphic fibre space where $D$ is divisor with conic singularities and let fibres $(X_s,D_s)$ are log Calabi-Yau pair .i.e $K_X+D$ is nummerically trivial, then we have ...
user21574
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fake Calabi-Yau threefold
(1) What is a "fake Calabi-Yau threefold"? Can I describe as a complex or symplectic manifold with trivial canonical bundle, but no compatible Kahler structure? Some mathematicians actually seem to ...
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Physical invariants of Calabi-Yau manifolds and G2 manifolds
Physicists said that for a given Calabi-Yau 3-fold with the topological Euler number $e$, $|e|/2$ corresponds to the number of generations of the elementary particles.
My question is: what ...
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Are there connections between Calabi-Yau manifolds and number theory?
I am interested in understanding whether there are any significant connections between Calabi-Yau manifolds and number theory. Calabi-Yau manifolds are central objects in algebraic geometry and string ...
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Contracting a family of rational curves in a Calabi Yau threefold
Suppose we have a Calabi-Yau 3-fold $X$ (not necessarily compact, over $\mathbb{C}$) that contains a ruled surface over a smooth curve $C$ of genus $g$. I am using a strong definition of a ruled ...
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Is Stenzel's Ricci-flat metric on $T^*\mathbb{CP}^n$ hyperkahler?
In a well-known paper, Stenzel constructed complete Ricci-flat Kahler metrics on the total spaces of cotangent bundles of $S^n$, $\mathbb{RP}^n,$ $\mathbb{CP}^n$, $\mathbb{HP}^n$, and $\mathbb{OP}^2$.
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Iterated integrals on higher dimensional Calabi-Yau manifolds?
I recently read about the construction of closed quasi-periodic differential forms on elliptic curves (1-dim Calabi-Yaus) via the Kronecker-Eisenstein series. I now wonder if similar constructions are ...
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A question about the proof of McLean's theorem: why is the space of $C^{k,\alpha}$ exact $p$-forms a Banach space?
In the famous paper "Deformations of Calibrated Submanifolds" by Robert McLean, he showed that given a smooth compact special Lagrangian $L$ in a Calabi-Yau manifold $(X^{2n},\omega,\Omega)$, there is ...
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Line bundles with vanishing cohomology on Calabi-Yau manifold
Suppose we have some line bundle $L(D)$ on Calabi-Yau threefold. Let's call this line bundle "rigid" if $H^0(X,L(D)) \simeq \mathbb{C}$ and $H^i(X,L(D))=0$ for $i=1,2,3$.
Is anything known about such ...
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Flat cohomology of an ordinary liftable Calabi-Yau threefold
Let $k$ be a perfect field of characteristic $p>0$ and consider an ordinary liftable Calabi-Yau threefold $X_{0}/k$. By this I mean that $H^{i}(X_{0},B_{X_{0}/k}^{j})=0$ for all $i\geq 0$ and $j\...
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Moduli space of K3 surfaces and Bogomolov-Tian-Todorov theorem
The famous Bogomolov-Tian-Todorov theorem says that the moduli space of Calabi-Yau manifold is smooth, that is locally a complex manifold. Doesn't this contradicts to the fact that the moduli space ...
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Is Gromov-Witten theory of Calabi-Yau threefolds of Type A trivial?
There are some Calabi-Yau threefolds that do not contain any rational curves, e.g. Calabi-Yau threefold of type A in the paper "Calabi-Yau threefolds of quotient type" by Oguiso and Sakurai.
My ...
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