# 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.

**2**

**1**answer

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

**1**

**0**answers

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

**9**

**0**answers

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

**4**

**1**answer

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

**2**

**0**answers

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

**5**

**0**answers

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

**7**

**1**answer

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

**6**

**0**answers

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

**3**

**0**answers

### Calabi $C^3$ estimate

**9**

**0**answers

### Higher homotopy groups of Calabi-Yaus

**5**

**1**answer

### Multiple mirrors phenomenon from SYZ and HMS perspective

**5**

**1**answer

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

**6**

**0**answers

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

**4**

**0**answers

### Canonical differential on K3 surface

**3**

**0**answers

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

**14**

**2**answers

### Deformations of Calabi-Yau manifolds

**7**

**1**answer

### Hodge Numbers and Leray Spectral Sequence

**1**

**0**answers

### A question about the proof of McLean's theorem: why is the space of $C^{k,\alpha}$ exact $p$-forms a Banach space?

**4**

**0**answers

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

**13**

**0**answers

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

**5**

**1**answer

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

**2**

**0**answers

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

**11**

**1**answer

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

**6**

**0**answers

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

**2**

**0**answers

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

**3**

**0**answers

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

**8**

**0**answers

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

**10**

**1**answer

### Calabi-Yau manifolds and knot theory

**5**

**0**answers

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

**7**

**0**answers

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

**2**

**1**answer

### Asymptotic formula for Ricci flat metric

**1**

**1**answer

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

**7**

**1**answer

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

**5**

**1**answer

### Lelong number of Ricci flat metric

**1**

**1**answer

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

**1**

**1**answer

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

**4**

**0**answers

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

**0**

**1**answer

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

**12**

**0**answers

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

**4**

**0**answers

### Calabi-Yau theorem on arithmetic variety

**9**

**0**answers

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

**6**

**0**answers

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

**0**

**1**answer

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

**2**

**0**answers

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

**15**

**3**answers

### Can Calabi-Yau manifolds have nonabelian discrete symmetry groups?

**1**

**0**answers

### Line bundles with vanishing cohomology on Calabi-Yau manifold

**4**

**2**answers

### Unique Kahler-Einstein metric $g$ with $\mathrm{Ricc}(g)=-g$ when first Chern class $C_1(M)<0$: $\mathrm{Ricc}(h)=-g\,\Rightarrow\,h=cg$ for $c>0$?

**2**

**0**answers

### Weil Petersson metric on moduli space of Calabi Yau manifolds

**4**

**1**answer

### BCOV's holomorphic anomaly equation at genus one

**7**

**1**answer