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seen Jul 29 at 1:14

Jul
1
awarded  ag.algebraic-geometry
Jun
29
comment Complex structure on $S^6$ gets published in Journ. Math. Phys
I am quite worried by the fact that the subbundle $H\subset TG_2$ that the author defines is not integrable. Just before (13) the author says that the Levi-Civita connection $\nabla_0$ preserves the splitting $TG_2=V\oplus H$, but this would certainly imply that $H$ is closed under Lie bracket.
Jun
22
comment Lie derivative and taking trace
If $X$ has a zero then there is a complex-valued function $u$ such that $X=g^{i\bar{j}}\partial_{\bar{j}}u \partial_i$, and so $\int_M X(f) \omega^n=-\int_X u\Delta f\omega^n=-\int_X ug\omega^n$.
Jun
17
comment Lie derivative and taking trace
Yes, if you allow non-local operators in your formula, such as the Green operator of $\omega$ (and then it is trivial to derive a formula for $X(f)$). If you insist on a purely local formula, then I am afraid the answer is no, because $X(f)$ involves only one derivative of $f$, while $g$ involves two derivatives. On the other hand, if all you care about is an integral relation between these quantities, then often you can do this, by using integration by parts (in particular you can do it if your vector field $X$ has a zero, in which case $X$ has a holomorphy potential).
Jun
13
revised Vafa's semi-Ricci flat metric
added 2 characters in body
May
15
awarded  Enlightened
May
15
awarded  Nice Answer
Apr
20
comment Acyclicity of the sheaf of real analytic differential forms
Cartan's paper can be downloaded here: archive.numdam.org/ARCHIVE/BSMF/BSMF_1957__85_/…
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 $S$?