bio | website | |
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location | ||
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visits | member for | 4 years, 4 months |
seen | 6 hours ago | |
stats | profile views | 2,264 |
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 $S$? |