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Mar
2
comment Why can we not always take a Kähler class to be in rational cohomology?
"may very well have empty intersection" is not correct since the $0$ vector is always in this intersection
Feb
22
awarded  Yearling
Feb
17
revised An identity for Futaki-Donaldson invariant
edited tags
Feb
16
comment Complex manifolds with trivial canonical bundle
See also the long list of references on page 1 of arxiv.org/pdf/1401.4797.pdf, which will provide you with many more examples of compact complex non-Kähler manifolds with trivial canonical bundle.
Feb
16
answered An identity for Futaki-Donaldson invariant
Feb
12
answered Computing the coefficients of the polynomial $\dim H^0(X,L^k)$ in non-smooth case
Feb
10
comment Obstructions to deformations of complex manifolds
For examples of obstructed deformations of quotients of $SL(2,\mathbb{C})$ see also this paper of Ghys perso.ens-lyon.fr/ghys/articles/deformationsstructures.pdf. This paper of Rollenske math.uni-bielefeld.de/~rollenske/papers/… seems also quite relevant.
Feb
5
comment Hermitian metric on conic Kaehler-Einstein setting
You just took your notations from page 16 here arxiv.org/pdf/1211.4669.pdf. I believe everything is explained there.
Feb
5
comment Hermitian metric on conic Kaehler-Einstein setting
This is certainly false if you don't impose any relation among $H$, $\omega$ and $S$, since as you wrote it now $H$ is an arbitrary Hermitian metric on $K_M^{-1}$.
Feb
5
comment When a Spherical variety is $K$-stable
K-stability depends on the choice of a polarization. What polarization do you want to choose?
Feb
4
comment Understanding a proof of a lemma in elliptic surfaces
Perhaps your advisor can provide you with more details, since he wrote the paper?
Feb
4
comment Hermitian metric on conic Kaehler-Einstein setting
What is the relation between $H$, $\omega$ and $S$?
Feb
4
comment Continuations of holomorphic functions on submanifolds to the total space
Just a comment about your second sentence: a connected closed complex submanifold of $\mathbb{C}^d$ is just a point. And extension of holomophic functions from a point becomes pretty trivial...
Jan
17
awarded  Popular Question
Jan
10
comment Ricci flow on non-compact manifold
Without extra assumptions, the answer is no even on $\mathbb{C}^n$.
Jan
6
awarded  Self-Learner
Jan
6
awarded  Revival
Jan
6
accepted Is S^2 x S^4 a complex manifold?
Jan
6
answered Is S^2 x S^4 a complex manifold?
Jan
6
accepted Moishezon manifolds with vanishing first Chern class