YangMills
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Unregistered User
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May 17 |
revised |
Dolbeault cohomology edited tags |
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May 15 |
answered | Dolbeault cohomology |
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May 8 |
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Converse to Milnor’s theorem on manifolds with nonnegative Ricci curvature. "cook one UP"... |
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Apr 27 |
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H^d[U(1)^n,U(1)] of the Borel cohomology and Chern-Simons theory @Idear: why do you keep capitalizing PHYSICS? |
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Apr 23 |
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Energy functional your Dirichlet energy is not correct! |
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Apr 19 |
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Jet differentials and hyperbolicity: possible mistake in the literature? I find it hard to believe that there is really a crucial mistake in the work of Demailly et al. It seems more likely that Sun's paper is not quite correct. I am particularly worried by the sentence "One can then compute... and see...". |
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Apr 14 |
awarded | ● Enlightened |
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Apr 14 |
awarded | ● Nice Answer |
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Mar 27 |
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Another reference request about dualizing sheaves for nodal surfaces This paper is also a classic: maths.ed.ac.uk/~aar/papers/durfee15.pdf |
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Mar 23 |
accepted | infimum of the Calabi energy in a given Kahler class |
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Mar 22 |
revised |
infimum of the Calabi energy in a given Kahler class added 704 characters in body |
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Mar 22 |
answered | infimum of the Calabi energy in a given Kahler class |
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Mar 22 |
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Sign convention in generalised Gauss-Bonnet In other words, Deane's comment was exactly what you needed!! |
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Mar 21 |
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Subadditivity of Kodaira dimension If $X$ is just a compact complex manifold (not Kähler), then the statement is false. There is an example in the book of K. Ueno, "Classification theory of algebraic varieties and compact complex spaces", see the reference on page 1 of this paper arxiv.org/abs/1204.3165. I am not aware of any Kähler counterexample. |
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Mar 18 |
accepted | Mukai-Umemura 3-fold and Kaehler-Einstein metrics |
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Mar 15 |
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Alexandrov space where a Yau’s inequality that holds on Riemannian manifold fails Also, how can you say that you know that the inequality does not hold on Alexandrov spaces when you have no such example? Maybe the inequality DOES hold on Alexandrov spaces! |
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Mar 15 |
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Alexandrov space where a Yau’s inequality that holds on Riemannian manifold fails duplicate of mathoverflow.net/questions/119592/… |
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Mar 1 |
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Must a hyperbolic cone over Riemannian manifold be manifold? Since you raised this question, can you please tell us why it must be a manifold? |
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Feb 22 |
awarded | ● Yearling |
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Feb 12 |
revised |
Are the Chern numbers of a hyperbolic-type compact complex manifold bounded in terms of the Euler number? edited tags |
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Feb 12 |
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Are the Chern numbers of a hyperbolic-type compact complex manifold bounded in terms of the Euler number? Proposition 3.13 in this paper of Catanese-Schneider dx.doi.org/10.1007/BF01444736 gives universal bounds for the Chern numbers (assuming $K_X$ ample like you want) in terms of $(−1)^n c^n_1=K^n_X$. Does this help? When $n=3$, you also have the Yau inequality which bounds −$c^3_1\leq(8/3)(−c_1)c_2$, but then? |
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Feb 11 |
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Are the Chern numbers of a hyperbolic-type compact complex manifold bounded in terms of the Euler number? In this related question mathoverflow.net/questions/26586/… Dmitri points out that the answer is definitely NO if you drop the assumption of negative first Chern class. |
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Feb 5 |
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Birational Automorphisms and infinite divisibility Lieberman's theorem was also proved independently and simultaneously by A. Fujiki here link.springer.com/article/10.1007%2FBF01403162 |
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Feb 4 |
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First eigenvalue of $\Delta$ on Kaehler manifold with $Ricci\ge k$. added 63 characters in body |
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Feb 4 |
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First eigenvalue of $\Delta$ on Kaehler manifold with $Ricci\ge k$. added 288 characters in body |
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Feb 1 |
accepted | First eigenvalue of $\Delta$ on Kaehler manifold with $Ricci\ge k$. |
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Feb 1 |
answered | First eigenvalue of $\Delta$ on Kaehler manifold with $Ricci\ge k$. |
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Jan 31 |
accepted | What is the Weitzenböck formula for the $\bar\partial$-Laplacian |
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Jan 31 |
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What is the Weitzenböck formula for the $\bar\partial$-Laplacian I meant to write "complex gradient of $f$", but I think it's clearer now. |
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Jan 31 |
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What is the Weitzenböck formula for the $\bar\partial$-Laplacian added 13 characters in body |
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Jan 31 |
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What is the Weitzenböck formula for the $\bar\partial$-Laplacian $\partial f$ is the $(1,0)$ part of the differential $1$-form $df$. I will correct my wrong wording now, sorry. |
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Jan 30 |
answered | What is the Weitzenböck formula for the $\bar\partial$-Laplacian |
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Jan 26 |
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Why is the Bochner formula on an Alexandrov space worse than on a Riemannian manifold? edited title |
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Jan 26 |
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Deformations of Kähler manifolds where Hodge decomposition fails? The paper of Popovici contained a mistake, so this theorem remains a conjecture. See here link.springer.com/article/10.1007/… |
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Jan 26 |
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Mirror symmetry for hyperkahler manifold I recommend you read section 7 of this paper of Gross arxiv.org/pdf/math/9809072.pdf, section 1 of Gross-Wilson arxiv.org/pdf/math/0008018v3.pdf, and this paper of Dolgachev arxiv.org/pdf/alg-geom/9502005v2.pdf |
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Jan 24 |
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Moishezon manifolds with vanishing first Chern class Thanks a lot, this is very interesting! |
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Jan 24 |
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Digital Copy of Kato’s Paper see also here (for bad news): mathoverflow.net/questions/96257/… |
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Jan 22 |
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Can you get an Enrique surface from quotient of Abelian surface? The answer is yes. For example, see Section 4 of this paper: arxiv.org/pdf/0909.5358.pdf |
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Jan 19 |
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What are the general techniques for proving a variety is not toric? It is definitely very easy to show that the automorphism group of the blowup of $\mathbb{P}^2$ in $s>3$ general points is discrete, since its Lie algebra is the space of holomorphic vector fields; on $\mathbb{P}^2$ this space has dimension $3$, and every time you blow up a point the dimension drops by one. |
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Jan 16 |
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Functorial properties of blow-up what is a diffeomorphism of singular varieties? |
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Jan 16 |
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Useless math that became useful Conic sections were apparently used by the Greeks (possibly Archimedes) in real life: en.wikipedia.org/wiki/Parabolic_reflector |
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Jan 12 |
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Uniqueness of Kähler form with same volume Keep in mind that in general noncompact Kahler manifolds two Kahler metric can have the same volume form without being equal (or isometric), for example the Taub-NUT metric on $\mathbb{C}^2$ and the standard flat metric have the same volume form. |
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Jan 10 |
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The symmetric group and the field with one element @Z254R: those two citations do not exist! I admit that I really don't get what you meant... |
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Jan 8 |
awarded | ● Nice Answer |
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Jan 5 |
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New grand projects in contemporary math just a minor comment about 3: Donaldson's article was actually written in 1996, and although it is supposed to be a reworking of his 1986 Fields Medallist lecture, the material on constant scalar curvature Kahler metrics (including the conjectures) is from 1996, which is roughly when Donaldson started thinking about those matters. |
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Dec 28 |
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elliptic regularity on manifolds Your assumptions imply that the function $u$ is in the Sobolev space $W^{2m,p}(M),$ and its $W^{2m,p}$ norm can be bounded in terms of its $L^q$ norm and the $L^p$ norm of $f$ (with a constant that depends on the geometry of $(M,g)$, on its dimension, on $p,q,m$). The proof of these facts is a simple application of the local results, using a partition of unity (as Paul Siegel says), and is something that you should really work out by yourself in detail at least once. |
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Dec 25 |
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Compact Complex n-folds with Betti numbers $b_1=b_2=b_n=0$ for $n >3$ oops, I guess I read the OP's condition as $b_1=b_2=b_3=...=b_n=0$, which is apparently not what was asked! |
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Dec 25 |
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Compact Complex n-folds with Betti numbers $b_1=b_2=b_n=0$ for $n >3$ yes, but it won't satisfy the OP's condition on the Betti numbers! |
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Dec 24 |
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Why the sectional curvatures assume maximum on holomorphic planes for positively curved Kaehler manifold? the proof that you want is on pages 154-155 there (even if you can't read French, I think you'll have no problem following the proof). Note that some inequalities on page 155 are wrong, and are corrected in the erratum (linked above). |
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Dec 22 |
awarded | ● Good Question |
