List questions from hodge-theory

Published on 22 Mar 2026 - 5:22

82

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

Published on 23 Mar 2026 - 4:39

227

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Regarding Hodge's theorem

Published on 23 Mar 2026 - 7:55

292

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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 22 Mar 2026 - 19:41

676

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Commutation of the covariant Hodge Laplacian with the covariant derivative

Published on 23 Mar 2026 - 3:13

594

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

Published on 23 Mar 2026 - 5:23

137

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Question in proof of Hodge decomposition theorem

Published on 22 Mar 2026 - 18:53

201

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

Published on 22 Mar 2026 - 20:47

84

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Local invariant cycles with integer coefficients

Published on 23 Mar 2026 - 7:14

2.1k

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Sign of codifferential

Published on 22 Mar 2026 - 22:45

2.7k

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Path to learning Hodge Theory via Voisin's text.

Published on 23 Mar 2026 - 6:55

115

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Systematic application of algebraic topology to energy minimization problems?

Published on 25 Mar 2026 - 6:20

88

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Star operator, exterior product

Published on 25 Mar 2026 - 5:05

530

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Analogies between Hodge conjecture and Tate conjecture

Published on 25 Mar 2026 - 1:35

627

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Deligne's theorem on the Leray spectral sequence and weights

Published on 25 Mar 2026 - 11:58

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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