All Questions
Tagged with calabi-yau reference-request
9 questions
19
votes
2
answers
8k
views
The canonical line bundle of a normal variety
I have heard that the canonical divisor can be defined on a normal variety X since the smooth locus has codimension 2. Then, I have heard as well that for ANY algebraic variety such that the canonical ...
- 2,215
13
votes
1
answer
1k
views
Today's world record on the Betti numbers of Calabi-Yau three-folds.
What are largest betti numbers $b_2$ and $b_3$ of three-dimensional Calabi-Yau manifolds that are discovered for today?
Is there some nice reference?
- 14.3k
9
votes
5
answers
2k
views
Why is the mirror of resolved conifold the deformed conifold?
I often see a sentence like "the mirror of resolved conifold is the deformed conifold" in physics literature. I would like to ask, in what sense is this true? What is known for mirror symmetry for ...
- 141
9
votes
3
answers
915
views
Why is the mirror of rigid Calabi-Yau threefold singularity theory?
Mirror symmetry relates two Calabi-Yau threefolds with mirrored Hodge diamonds. Since Calabi-Yau threefold is Kahler, this naive correspondence does not hold for rigid Calabi-Yau threefolds. Here ...
- 583
5
votes
1
answer
320
views
$K_X+B \equiv 0$ implies $K_X + B \sim_\mathbb{Q} 0$?
Let $(X,B)$ be a projective log canonical pair (here I mean $B \geq 0$). Assume that the coefficients of $B$ are rational, and that $K_X+B \equiv 0$. Is it true that $K_X + B \sim_\mathbb{Q} 0$? I ...
- 625
5
votes
0
answers
300
views
Examples or references for this claim about elliptic Calabi-Yau threefolds
In this article (page 2) , the authors say:
"it is expected, based on known examples, that Calabi–Yau threefolds of large Picard
rank are always elliptically fibered, perhaps after flopping a ...
- 1,841
2
votes
1
answer
323
views
Special Lagrangians and fat
I am unable to find the MO comments about the first use of the phrase "fat slags" in an article. On page 26 of this we find "these correspond to thickenings of the
corresponding special Lagrangian (...
1
vote
0
answers
270
views
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 ...
1
vote
0
answers
100
views
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 ...
- 231