List questions from hodge-theory

Published on 25 Mar 2026 - 19:10

63

Views

Given a smooth 2-form $\varphi$ on a punctured Riemann surface, is there $\nu$ of type (1,0) such that $\varphi=d\nu$?

Published on 02 Feb 2015 - 20:16

275

Views

Why is the $ \mathbb{Z} $ - Hodge conjecture false?

Published on 08 Mar 2015 - 13:05

372

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Sign problems in complex computations

Published on 11 Mar 2015 - 15:19

546

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Could you explain the failure of the Hodge decomposition to exist for non-compact manifolds?

Published on 26 Mar 2026 - 6:22

171

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A simple question about rational Hodge conjecture

Published on 14 Mar 2015 - 22:54

42

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Example of non interchangeability of the order of taking graded moduls with respect to three filtrations

Published on 20 Mar 2026 - 13:28

188

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Hodge star/ Technical question

Published on 18 Apr 2015 - 20:22

120

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Why are algebraic cycles rational?

Published on 27 Apr 2015 - 17:36

120

Views

Cohomology of conic bundle 3-folds

Published on 08 May 2015 - 9:20

614

Views

The adjoint of left exterior multiplication by $\xi^\flat$ for Hodge star operator

Published on 17 May 2015 - 0:59

99

Views

Proving that $\phi$ is orthogonal to the harmonic forms given $\int\phi \;d\mathrm{vol}$.

Published on 21 May 2015 - 14:31

249

Views

Automorphisms of manifold vs automorphisms of Hodge structure

Published on 26 May 2015 - 8:27

441

Views

Hodge self-duality in Minkowski spacetime

Published on 26 Mar 2026 - 9:40

319

Views

Exercise about Hodge Star Operator on $\Lambda^{p,q}$

Published on 26 Mar 2026 - 14:28

List Question

In what sense is $p$-adic Hodge theory related to ordinary (complex) Hodge theory?

Given a smooth 2-form $\varphi$ on a punctured Riemann surface, is there $\nu$ of type (1,0) such that $\varphi=d\nu$?

Why is the $ \mathbb{Z} $ - Hodge conjecture false?

Sign problems in complex computations

Could you explain the failure of the Hodge decomposition to exist for non-compact manifolds?

A simple question about rational Hodge conjecture

Example of non interchangeability of the order of taking graded moduls with respect to three filtrations

Hodge star/ Technical question

Why are algebraic cycles rational?

Cohomology of conic bundle 3-folds

The adjoint of left exterior multiplication by $\xi^\flat$ for Hodge star operator

Proving that $\phi$ is orthogonal to the harmonic forms given $\int\phi \;d\mathrm{vol}$.

Automorphisms of manifold vs automorphisms of Hodge structure

Hodge self-duality in Minkowski spacetime

Exercise about Hodge Star Operator on $\Lambda^{p,q}$

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