List questions from hodge-theory

Published on 23 Feb 2026 - 2:40

51

Views

Induced isomorphism between $H^{1,0}(X)$ and $H^{1,0}(Y)$ implies the induced isomorphism between $H^{0,1}(X)$ and $H^{0,1}(Y)$?

Published on 25 Mar 2026 - 1:28

196

Views

The cohomological self-dual and anti-self-dual decomposition

Published on 13 Mar 2019 - 1:47

764

Views

Real Hodge structures and representations of the Deligne torus

Published on 01 Apr 2019 - 13:55

288

Views

Hodge theory: $\Delta \alpha = 0$ iff $d\alpha = d^* \alpha = 0$ on a noncompact manifold?

Published on 25 Mar 2026 - 15:54

1.1k

Views

What is an example of harmonic form on a compact manifold?

Published on 25 Mar 2026 - 11:33

158

Views

Hodge star operator of $\frac{\omega^k}{k!}$ is $\frac{\omega^{n-k}}{(n-k)!}$

Published on 25 Mar 2026 - 12:41

70

Views

Hard Lefschetz and Hodge Decoposition

Published on 25 Mar 2026 - 12:43

43

Views

Higgs Bundle with value not in canonical bundle.

Published on 04 Jul 2019 - 2:00

667

Views

Has anyone got a reference as to why étale Galois representations are de Rham?

Published on 25 Mar 2026 - 1:16

249

Views

Finding the Hodge dual of $dy$

Published on 03 Sep 2019 - 18:44

74

Views

Splitting of a short exact sequence in cohomology due to torsion

Published on 12 Sep 2019 - 21:37

999

Views

Dolbeault cohomology on torus

Published on 18 Mar 2014 - 22:21

470

Views

Construction of Hodge decomposition

Published on 26 Mar 2014 - 2:57

189

Views

A question on harmonic two-forms

Published on 27 May 2014 - 5:24

List Question

Is the shear of a vector field related to the exterior differential?

Induced isomorphism between $H^{1,0}(X)$ and $H^{1,0}(Y)$ implies the induced isomorphism between $H^{0,1}(X)$ and $H^{0,1}(Y)$?

The cohomological self-dual and anti-self-dual decomposition

Real Hodge structures and representations of the Deligne torus

Hodge theory: $\Delta \alpha = 0$ iff $d\alpha = d^* \alpha = 0$ on a noncompact manifold?

What is an example of harmonic form on a compact manifold?

Hodge star operator of $\frac{\omega^k}{k!}$ is $\frac{\omega^{n-k}}{(n-k)!}$

Hard Lefschetz and Hodge Decoposition

Higgs Bundle with value not in canonical bundle.

Has anyone got a reference as to why étale Galois representations are de Rham?

Finding the Hodge dual of $dy$

Splitting of a short exact sequence in cohomology due to torsion

Dolbeault cohomology on torus

Construction of Hodge decomposition

A question on harmonic two-forms

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