All Questions
10 questions
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
12
votes
1
answer
1k
views
Why Yau's theorem implies the existence of hyperkähler metric on complex symplectic manifolds?
Every expository article on hyperkähler manifolds that I have read states without detailed proof the following fact:
It follows from Yau's theorem (i.e. a compact Kähler manifold $M$ with $c_1(M)=0$ ...
- 1,804
6
votes
1
answer
413
views
A technical question in Feix's construction of hyperkahler metric on cotangent bundles
I am now reading Feix's paper Hyperkahler metrics on cotangent bundles
and I have a technical question to ask.
In his paper, for an analytic Kähler manifold $(X,J,\omega)$, Feix considered its ...
- 783
4
votes
2
answers
668
views
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 $c>0$?
On a compact Kahler manifold, let $g$ be the unique Kahler-Einstein metric with $\mathrm{Ricc}(g)=-g$, proved to exist by Yau and Aubin when the first Chern class $C_1(M)<0$.
Question: Does $g$ ...
- 376
3
votes
1
answer
818
views
Questions on the Hodge Dual of the Kähler Class
Let $M$ be a compact complex surface, i.e., a complex manifold with complex dimension two. Also, let us denote its Kähler metric by $g$ and its Kähler form by $K$. Let us denote the Kähler class by $[...
- 424
3
votes
0
answers
150
views
Why does the bisectional curvature blow up?
Suppose we have $X = X_1 \times X_2$, where $X_1$ is a Calabi-Yau manifold (i.e. $c_1(X_1) = 0$) and $X_2$ is a compact Kähler manifold of $c_1(X_2) < 0$. We can consider the metric $\omega(t, x_1, ...
- 59
2
votes
1
answer
408
views
Asymptotic formula for Ricci flat metric
Let $(\mathcal X,\mathcal D)\to T$ be a surjective holomorphic fibre space of K\"ahler manifolds of pairs such that fibers $(X_s,D_s)$ admit Ricci flat metric in bounded geometric sense (conic, ...
- 63
1
vote
1
answer
474
views
Fibration when central fibre is a Calabi-Yau variety with canonical singularities
Let $f\colon X\to Y$ be a surjective proper holomorphic fibre space such that $X$ and $Y$ are projective varieties and central fibre $X_0$ is Calabi-Yau variety with canonical singularities, then can ...
user21574
0
votes
1
answer
522
views
Canonical metric on moduli space of singular Calabi-Yau varieties
Let $\pi:X\to Y$ be a surjective holomorphic map with connected fibers
and let fibers are singular Calabi-Yau varieties (i.e. numerical dimension is zero) then is it possible to construct canonical ...
user21574
0
votes
1
answer
377
views
Weil-Petersson metric is quasi isometric with which model?
Let $\mathcal M_g$ be the moduli space of curves of genus $g$. If we take $X^{reg}=X\setminus D$, where D is a divisor with normal crossings. Endow
$X^{reg}$ with a complete Kahler metric which has a ...
user21574