List questions from hodge-theory

Published on 21 Apr 2026 - 10:26

89

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Why $H_{dR}^1(M) \simeq \mathbb R^n$ when $H_1(M,\mathbb Z)$ has $n$ generators?

Published on 29 Apr 2026 - 12:47

233

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Regarding Hodge's theorem

Published on 22 Apr 2026 - 6:07

299

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Let $M$ is compact Riemann surface, if $\omega$ is a 2-form and $\int_{M} \omega =0$ then there exists a smooth function $f$ such that $\omega=d*df$

Published on 10 May 2026 - 10:58

683

Views

Commutation of the covariant Hodge Laplacian with the covariant derivative

Published on 06 May 2026 - 13:44

599

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Every $L^2$ function is the divergence of a $L^2$ vector field

Published on 05 May 2026 - 7:03

142

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Question in proof of Hodge decomposition theorem

Published on 06 May 2026 - 14:20

206

Views

Lefschetz (1,1) theorem for quasi-projective varieties

Published on 05 May 2026 - 16:06

91

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Local invariant cycles with integer coefficients

Published on 07 May 2026 - 11:00

2.1k

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Sign of codifferential

Published on 05 May 2026 - 2:52

2.7k

Views

Path to learning Hodge Theory via Voisin's text.

Published on 06 May 2026 - 10:20

118

Views

Systematic application of algebraic topology to energy minimization problems?

Published on 22 Apr 2026 - 21:23

94

Views

Star operator, exterior product

Published on 23 Apr 2026 - 22:06

533

Views

Analogies between Hodge conjecture and Tate conjecture

Published on 24 Apr 2026 - 0:23

630

Views

Deligne's theorem on the Leray spectral sequence and weights

Published on 23 Apr 2026 - 4:42

List Question

How are rational algebraic Hodge classes of type $ (p,p) $ defined?

Why $H_{dR}^1(M) \simeq \mathbb R^n$ when $H_1(M,\mathbb Z)$ has $n$ generators?

Regarding Hodge's theorem

Let $M$ is compact Riemann surface, if $\omega$ is a 2-form and $\int_{M} \omega =0$ then there exists a smooth function $f$ such that $\omega=d*df$

Commutation of the covariant Hodge Laplacian with the covariant derivative

Every $L^2$ function is the divergence of a $L^2$ vector field

Question in proof of Hodge decomposition theorem

Lefschetz (1,1) theorem for quasi-projective varieties

Local invariant cycles with integer coefficients

Sign of codifferential

Path to learning Hodge Theory via Voisin's text.

Systematic application of algebraic topology to energy minimization problems?

Star operator, exterior product

Analogies between Hodge conjecture and Tate conjecture

Deligne's theorem on the Leray spectral sequence and weights

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