# 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.

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### When do crepant resolutions of quotients of Calabi-Yau varieties exist?

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### Why does the bisectional curvature blow up?

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### How to find a rational $\mathbb{F}_{\!q}$-curve on a quite classical Calabi–Yau threefold?

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### Calabi-Yau structures on dg-categories

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### Embedding Calabi-Yau manifolds in projective space

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### (1/2) K3 surface or half-K3 surface: Ways to think about it?

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### Explicitly computing Donaldson-Thomas invariants (of CY 3-folds)

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### Is there a Calabi-Yau threefold with $h^{1,1}=1$ and $h^{1,2}=0$?

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### Examples of Calabi-Yau manifolds with $\mathbb{T}^2$ symmetry

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### geometrical or physical interpretation of second Chern classes of Calabi-Yau threefold

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### A Calabi-Yau manifold with finite simple fundamental group?

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### What is the geometrical meaning of higher Chern forms and classes?

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### Can we define topological quantum field theories on Calabi-Yau manifolds?

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### Calabi $C^3$ estimate

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### Higher homotopy groups of Calabi-Yaus

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### Multiple mirrors phenomenon from SYZ and HMS perspective

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### $K_X+B \equiv 0$ implies $K_X + B \sim_\mathbb{Q} 0$?

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### Can the base of an elliptically fibered Calabi-Yau threefold be an Enriques surface?

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### Canonical differential on K3 surface

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### Open Gromov-Witten invariants via lozalization with $\mathbb{C}^{*}$ (not $S^1$) action

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### Deformations of Calabi-Yau manifolds

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### Hodge Numbers and Leray Spectral Sequence

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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?

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### Kuranishi family and smoothing of Calabi-Yau n-fold

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### Kähler-Ricci flow approach for Beauville-Bogomolov type decomposition?

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### Is there any relativistic interpretation on considering Kaehler-Einstein metrics and Calabi-Yau manifolds?

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### SYZ conjecture for varieties of general type or Fano

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### Large Complex Structure Limit of Calabi-Yau family and uniqueness of limit

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### Analytical point of view of Kawamata's Unipotent reduction condition for Calabi-Yau family

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### Calibrated submanifolds in Spin(7) and Calabi-Yau threefold

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### What is the meaning of rationality for these series?

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### Any progress on Strominger-Yau and Zaslow conjecture?

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### Calabi-Yau manifolds and knot theory

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### connectedness of moduli space of Calabi-Yau 3-folds by symplectic surgery theory

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### Examples of Maximal degeneration of Deligne on Calabi-Yau degeneration

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### Asymptotic formula for Ricci flat metric

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### Constraints on the base of an elliptically fibered Calabi-Yau threefold

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### How do you get the spectral curve from a Calabi-Yau?

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### Lelong number of Ricci flat metric

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### Fibration when central fibre is a Calabi-Yau variety with canonical singularities

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### Find the Picard Fuchs operator of a four parameter fundamental period

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### Matsushita theorem on framed variety (X,D)

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### Canonical metric on moduli space of singular Calabi-Yau varieties

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### Elkies' supersingularity theorem in higher dimension (in terms of the associated Newton polygon)

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### Calabi-Yau theorem on arithmetic variety

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### Holomorphic vector fields on compact complex manifolds with trivial canonical bundle

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### Moduli space of log Calabi-Yau varieties exists?

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### Weil-Petersson metric is quasi isometric with which model?

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### Ricci flat metric on pair (X,D)

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