List questions from hodge-theory

Published on 09 Apr 2026 - 9:34

53

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 13 Apr 2026 - 16:51

199

Views

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

Published on 14 Apr 2026 - 5:13

767

Views

Real Hodge structures and representations of the Deligne torus

Published on 13 Apr 2026 - 5:24

290

Views

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

Published on 16 Apr 2026 - 1:04

1.1k

Views

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

Published on 10 Apr 2026 - 1:31

160

Views

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

Published on 14 Apr 2026 - 20:35

72

Views

Hard Lefschetz and Hodge Decoposition

Published on 12 Apr 2026 - 5:49

46

Views

Higgs Bundle with value not in canonical bundle.

Published on 13 Apr 2026 - 2:46

669

Views

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

Published on 09 Apr 2026 - 19:24

255

Views

Finding the Hodge dual of $dy$

Published on 16 Apr 2026 - 23:35

77

Views

Splitting of a short exact sequence in cohomology due to torsion

Published on 14 Apr 2026 - 23:23

1k

Views

Dolbeault cohomology on torus

Published on 14 Apr 2026 - 8:40

474

Views

Construction of Hodge decomposition

Published on 13 Apr 2026 - 2:43

193

Views

A question on harmonic two-forms

Published on 12 Apr 2026 - 22:04

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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