All Questions
7 questions with no upvoted or accepted answers
14
votes
0
answers
577
views
State of the art of BPS and Donaldson-Thomas invariants for toric Calabi-Yau threefolds
I am trying to understand what has been done with regards to computing BPS invariants and Donaldson-Thomas type invariants of Calabi-Yau threefolds. To make the question more focused, let's say that I ...
- 509
13
votes
0
answers
743
views
Kähler-Ricci flow approach for Beauville-Bogomolov type decomposition?
Is there any Kähler Ricci flow method for solving structure theorems in Algebraic geometry
In fact If $X$ be a Calabi-Yau manifold then we can descend the Kähler Ricci flow to its finite etale ...
user21574
7
votes
0
answers
760
views
Examples of Maximal degeneration of Deligne on Calabi-Yau degeneration
Pierre Deligne in his celebrated paper entitling "Local behavior of Hodge structures at infinity" introduced Maximal degenerations of Calabi-Yau manifolds.
Let $\pi:X\to \mathbb C^*$ be a family of ...
user21574
6
votes
0
answers
509
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Moduli space of log Calabi-Yau varieties exists?
Let $\mathcal M^{(X,D)}$ be a moduli space of pair varieties $(X,D)$ which $K_X+D$ is trivial and $D$ is a divisor with conic singularities on Kaehler variety $X$. I am looking for a proof that such ...
user21574
4
votes
0
answers
255
views
Matsushita theorem on framed variety (X,D)
I have a question about fibrations on Irreducible log holomorphic symplectic manifolds. Lets give some introduction
Motivation; A holomorphic symplectic manifold (HSM) is a $2n$-dimensional compact K\...
user21574
4
votes
0
answers
581
views
Calabi-Yau theorem on arithmetic variety
Let $\mathcal X\to \mathrm{Spec}(\mathcal O_K)=C$ be an arithmetric projective variety over $C$ , where $\mathcal O_K$, ring of number filed $K$. Let $\omega$ be a Kähler current of $\mathcal X(\...
user21574
3
votes
0
answers
209
views
Proof of the existence of a mirror Calabi–Yau manifold
Let $X$ be a Calabi–Yau threefold. Here, Calabi–Yau is understood to a mean a smooth simply connected projective threefold with $h^1(\mathcal{O}_X) = h^2(\mathcal{O}_X)=0$ and holomorphically trivial ...
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