scholarly journals Opposite filtrations, variations of Hodge structure, and Frobenius modules

2004 ◽  
pp. 19-43 ◽  
Author(s):  
Javier Fernandez ◽  
Gregory Pearlstein
Keyword(s):  
Hodge Structure ◽  
Variations Of Hodge Structure

scholarly journals On the equidistribution of some Hodge loci

2020 ◽  
Vol 2020 (762) ◽  
pp. 167-194
Author(s):  
Salim Tayou
Keyword(s):  
Hodge Structure ◽  
K3 Surfaces ◽  
Elliptic Fibrations ◽  
Projective Curves ◽  
Variations Of Hodge Structure

AbstractWe prove the equidistribution of the Hodge locus for certain non-isotrivial, polarized variations of Hodge structure of weight 2 with {h^{2,0}=1} over complex, quasi-projective curves. Given some norm condition, we also give an asymptotic on the growth of the Hodge locus. In particular, this implies the equidistribution of elliptic fibrations in quasi-polarized, non-isotrivial families of K3 surfaces.

scholarly journals Lowest weights in cohomology of variations of Hodge structure

2012 ◽  
Vol 206 ◽  
pp. 1-24
Author(s):  
Chris Peters ◽  
Morihiko Saito
Keyword(s):  
Open Subset ◽  
Hodge Structure ◽  
Analytic Space ◽  
Mixed Hodge Structure ◽  
Zariski Open Subset ◽  
Weight Part ◽  
Variation Of Hodge Structure ◽  
Local Monodromy ◽  
Variations Of Hodge Structure ◽  
Complex Analytic Space

AbstractLetXbe an irreducible complex analytic space withj:U ↪ Xan immersion of a smooth Zariski-open subset, and let 𝕍 be a variation of Hodge structure of weightnoverU. Assume thatXis compact Kähler. Then, provided that the local monodromy operators at infinity are quasi-unipotent,IHk(X, 𝕍) is known to carry a pure Hodge structure of weightk+n, whileHk(U, 𝕍) carries a mixed Hodge structure of weight at leastk+n. In this note it is shown that the image of the natural mapIHk(X, 𝕍) →Hk(U, 𝕍) is the lowest-weight part of this mixed Hodge structure. In the algebraic case this easily follows from the formalism of mixed sheaves, but the analytic case is rather complicated, in particular when the complementX — Uis not a hypersurface.

On Motivic Realizations of the Canonical Hermitian Variations of Hodge Structure of Calabi–Yau Type over type Domains

2019 ◽  
Vol 62 (1) ◽  
pp. 209-221
Author(s):  
Zheng Zhang
Keyword(s):  
Hodge Structure ◽  
Short Note ◽  
Symmetric Domain ◽  
Algebraic Varieties ◽  
Irreducible Factor ◽  
Variations Of Hodge Structure

AbstractLet${\mathcal{D}}$be the irreducible Hermitian symmetric domain of type$D_{2n}^{\mathbb{H}}$. There exists a canonical Hermitian variation of real Hodge structure${\mathcal{V}}_{\mathbb{R}}$of Calabi–Yau type over ${\mathcal{D}}$. This short note concerns the problem of giving motivic realizations for ${\mathcal{V}}_{\mathbb{R}}$. Namely, we specify a descent of${\mathcal{V}}_{\mathbb{R}}$from$\mathbb{R}$to$\mathbb{Q}$and ask whether the$\mathbb{Q}$-descent of${\mathcal{V}}_{\mathbb{R}}$can be realized as sub-variation of rational Hodge structure of those coming from families of algebraic varieties. When$n=2$, we give a motivic realization for ${\mathcal{V}}_{\mathbb{R}}$. When$n\geqslant 3$, we show that the unique irreducible factor of Calabi–Yau type in$\text{Sym}^{2}{\mathcal{V}}_{\mathbb{R}}$can be realized motivically.

Variations of Hodge structure of maximal dimension

1989 ◽  
Vol 58 (3) ◽  
pp. 669-694 ◽  
Author(s):  
James A. Carlson ◽  
Aznif Kasparian ◽  
Domingo Toledo
Keyword(s):  
Hodge Structure ◽  
Maximal Dimension ◽  
Variations Of Hodge Structure
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