All Questions
8 questions
1
vote
0
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123
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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 ...
- 71
8
votes
3
answers
918
views
Contracting a rational curve in a Calabi-Yau threefold
Let $X$ be a Calabi-Yau threefold and $C \subset X$ be a rational curve with $N_{C/X}\cong \mathcal{O}\oplus \mathcal{O}(-2)$. Can one contract the curve $C$? Assuming the answer is yes, what kind of ...
- 81
4
votes
0
answers
182
views
Kuranishi family and smoothing of Calabi-Yau n-fold
Consider $X$ be a Calabi-Yau n-fold with at
most one ordinary double point singularity. Suppose $X$ is smoothable. Then it is known that the Kuranishi family of $X$ is a smoothing of $X$.
Now, ...
- 81
2
votes
0
answers
511
views
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
4
votes
2
answers
558
views
Factoriality of one-nodal Calabi-Yau threefolds
Let $X$ be a projective Calabi-Yau threefold with a single ordinary double point at $x \in X$, and smooth elsewhere. Is $X$ necessarily factorial?
I suspect that the answer is "yes", for the ...
- 884
12
votes
0
answers
580
views
Cohomology and conifold transition for the quintic
Let $Y\subset \mathbb{C}P^4$ be the quintic threefold given by the equation $$X^5_0+X^5_1+X^5_2+X^5_3+X^5_4+5X_0X_1X_2X_3X_4=0$$
it has 125 singular points whose links are homeomorphic to $S^2\times S^...
- 9,870
4
votes
1
answer
143
views
Singularities induced by the toric ambient spaces
Let $\Delta \subset \mathbb{R}^4$ be a (reflexive) polytope and $X$ be the hypersurfacedefined by a generic section of the any-canonical bundle of the toric variety $\mathbb{P}_{\Delta}$. Are there ...
- 41
4
votes
2
answers
627
views
The link of a singular quintic hypersurface in CP^4
Given a family of quintic hypersurfaces in $\mathbb{CP}^4$ by
$x_1^5+x_2^5+x_3^5+x_4^5+x_5^5+(5+\epsilon)x_1x_2x_3x_4x_5$
we get a singular variety for $\epsilon=0$ with 125 singular points.
I know ...
- 93