Complex multiplication, Griffiths-Yukawa couplings, and rigidity for families of hypersurfaces

DOI10.1090/S1056-3911-05-00400-5zbMath1086.14029arXivmath/0307398MaRDI QIDQ5316106

Kang Zuo, Eckart Viehweg

Publication date: 12 September 2005

Published in: Journal of Algebraic Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307398

Mathematics Subject Classification ID

Families, moduli, classification: algebraic theory (14J10) Variation of Hodge structures (algebro-geometric aspects) (14D07) Generalizations (algebraic spaces, stacks) (14A20)

Related Items (12)

Infinitesimal variation functions for families of smooth varieties ⋮ Transcendence and CM on Borcea-Voisin towers of Calabi-Yau manifolds ⋮ Maximal families of Calabi-Yau manifolds with minimal length Yukawa coupling ⋮ K3 surfaces with algebraic period ratios have complex multiplication ⋮ On Shimura subvarieties generated by families of abelian covers of \(\mathbb{P}^1\) ⋮ A note on varieties of weak CM-type ⋮ GOOD REDUCTION AND CYCLIC COVERS ⋮ Rigidity of subfamilies of hypersurfaces in \(\mathbb P^n\) with maximal length of Griffiths-Yukawa coupling ⋮ Arakelov-Parshin rigidity of towers of curve fibrations ⋮ A Transcendence Criterion for CM on Some Families of Calabi–Yau Manifolds ⋮ On the negativity of moduli spaces for polarized manifolds ⋮ Shimura varieties and abelian covers of the line

Cites Work

• Algebraic cycles on Abelian varieties of Fermat type
• Higgs bundles and local systems
• Half twists and the cohomology of hypersurfaces
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Discriminant complements and kernels of monodromy representations
• Shafarevich's conjecture for CY manifolds I
• A note of Shimura's paper: Discontinuous groups and Abelian varieties
• The complex hyperbolic geometry of the moduli space of cubic surfaces
• Harmonic Bundles on Noncompact Curves
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