# Questions tagged [hodge-theory]

The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.

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### Integral lattice in noncommutative Hodge theory

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### Optimality condition of the harmonic form representatives of a homology class

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### Period map for $\partial\bar\partial$-manifolds

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### Fibers of period map

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### Definition of rational equivalence

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### Understanding the mixed Hodge structure on D-modules on $\mathbb{C}$

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### Closed algebraic subset dominating a curve

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### reference to a theorem about a product of harmonic and parallel forms

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### Relations between the morphic cohomology and Hodge theory

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### Do we have Hodge symmetry for char $p$?

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### Non Abelian Hodge theory: underlying structure holomorphic vector bundles

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### Is the dimension of the pieces of a mixed Hodge structure constant under smooth deformations?

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### Log-concavity of matroids: characterization of equality?

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### Cycle class map for singular varieties

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### Generalization of the Leray-Hirsch theorem

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### Is there a classification of non-simple Jacobians?

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### Tangential harmonic $1$-forms are pullbacks of harmonic functions

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### When do flat holomorphic connections exist?

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### Criterion for triviality of monodromy in smooth families

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### Does the Hodge decomposition hold for equivariant differential forms?

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### Is the abelian category of pure Hodge modules semi-simple?

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### Is the category of pure Hodge structures abelian semi-simple? [duplicate]

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### Is the Hodge bundle a holomorphic vector bundle?

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### Hodge theoretic properties of intersection cohomology

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### What makes a Kähler manifold projective?

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### A contradiction caused by the Kähler identity and the formal adjoint relation

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### Automorphism of integral Hodge structures

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### Is every $\omega\in H^0(U,\Omega_U^n)$ representable in $H^n(U,\mathbb{C})$ by an element from $H^0(X,\Omega_X^n(\log D))$?

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### Computing mixed hodge structure using different extension of the constant sheaf

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### How does the MHS on $H_Y^i(X)$ behave with respect to the Thom isomorphism?

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### Degeneration twisted Hodge to de Rham spectral sequence

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### Is there a way to describe the image of the $n$-fold residue map from $H^0(Y,\Omega_Y^n(\log E))$?

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### Does the Jacobian ring of a weighted projective hypersurface determine it up to isomorphism?

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### Is there a proper smooth variety in characteristic $p$ whose Hodge-to-de Rham spectral sequence does not degenerate at $E_1$?

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### Quasi-unipotent monodromy for variation of Landau-Ginzburg cohomology

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### Using principal polarisation to "cancel" Jacobian summands in isomorphism

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### cycle class in the cohomology of the nearby fibre

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### rational Hodge structure of spectral curve and Prym variety

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### Is there a direct way to show Fano surface of lines and conics on the pairs of Fano threefolds isomorphic?

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### A Green's function for the Laplacian on k-forms

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### Hodge structure and rational coefficients

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### Can every Hodge structure be polarized?

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### multiplicative structure on the monodromy weight filtration spectral sequence

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### What is the meaning of the monodromy theorem in Hodge theory?

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### Period map on non-Kähler manifold

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### Do Poincaré residue and integrable log connection commute?

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### Period domain closure and mixed Hodge structures

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### Can logarithmic connection operate on currents?

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### Can logarithmic connection on holomorphic vector bundle induce logarithmic connection on dual bundle?

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