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Inventiones Mathematicae, ISSN 0020-9910, 06/2017, Volume 208, Issue 3, pp. 677 - 713
We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more... 
14F10 | 14D07 | 14E30 | 14D06 | CANONICALLY POLARIZED VARIETIES | MATHEMATICS | POSITIVITY | STABILITY | Sheaves
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2013, Volume 162, Issue 12, pp. 2077 - 2148
We study horizontal subvarieties Z of a Griffiths period domain \mathbf {D} . If Z is defined by algebraic equations, and if Z is also invariant under a large... 
32G20 | 32M15 | 14D07
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2012, Volume 161, Issue 11, pp. 2167 - 2206
Andre used Hodge-theoretic methods to show that in a smooth proper family X B of varieties over an algebraically closed field k of characteristic zero, there... 
MATHEMATICS | PICARD NUMBER | F-ISOCRYSTALS | SURFACES | 14C25 | 14D07 | 14F30 | 14F25
Journal Article
Bollettino dell'Unione Matematica Italiana, ISSN 1972-6724, 3/2019, Volume 12, Issue 1, pp. 133 - 144
In this note we survey recent results on the extrinsic geometry of the Jacobian locus inside $$\mathsf {A}_g$$ A g . We describe the second fundamental form of... 
32G20 | 14H15 | 14D07 | 14C30 | Mathematics, general | Mathematics | 14H40 | 14H10
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 8/2018, Volume 289, Issue 3, pp. 1325 - 1355
We study periods and regulators of a certain class of fibrations of varieties whose relative $$H^1$$ H1 has multiplication by a number field. Both are written... 
Hypergeometric functions | Periods | Regulators | 11G15 | 14D07 | Complex multiplication | 33C20 (primary) | Mathematics, general | Mathematics | 14K22 (secondary) | 19F27 | HODGE-MODULES | MATHEMATICS
Journal Article
Mathematische Annalen, ISSN 0025-5831, 6/2012, Volume 353, Issue 2, pp. 633 - 661
On construit des variétés projectives lisses complexes de dimension 3 à 6 munies de variations de structure de Hodge, en généralisant une construction que J.... 
Mathematics, general | Mathematics | 55N33 | 14D07 | 14D05
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 11/2013, Volume 162, Issue 14, pp. 2797 - 2813
We show that any smooth complex projective variety whose fundamental group has a complex representation with infinite image must have a nonzero symmetric... 
MATHEMATICS | BUNDLES | REPRESENTATIONS | MAPS | SPACES | FAMILIES | VARIETIES | HYPERBOLICITY | 14F35 | 14D07
Journal Article
Mathematische Annalen, ISSN 0025-5831, 8/2017, Volume 368, Issue 3, pp. 1311 - 1332
We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the... 
32G20 | Mathematics, general | Mathematics | 14D07 | 14G40 | MATHEMATICS | VARIETIES | MANIFOLDS | CURVES | FAMILIES | SHEAVES | Equality
Journal Article
Michigan Mathematical Journal, ISSN 0026-2285, 11/2011, Volume 60, Issue 3, pp. 661 - 673
Journal Article
Nagoya mathematical journal, ISSN 0027-7630, 06/2012, Volume 206, pp. 39 - 66
We prove a Noether-Lefschetz type theorem for varieties of r-planes in complete intersections. We then use it to study the Abel-Jacobi map of planes on a... 
MATHEMATICS | FANO | LINES | 14D05 | 14D07 | 14C22
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 02/2019, Volume 136, pp. 14 - 30
Any irreducible Dynkin diagram Δ is obtained from an irreducible Dynkin diagram Δh of type ADE by folding via graph automorphisms. For any simple complex Lie... 
Calabi–Yau threefolds | Hodge theory | Global quotient stacks | Integrable systems | Hitchin systems | MATHEMATICS | DUALITY | Calabi-Yau threefolds | PHYSICS, MATHEMATICAL
Journal Article
Canadian mathematical bulletin, ISSN 0008-4395, 09/2018, Volume 61, Issue 3, pp. 659 - 672
We extend the infinitesimal Torelli theorem for smooth hypersurfaces to nodal hypersurfaces. 
Nodal hypersurface | Torelli theorem | Deformation | MATHEMATICS | nodal hypersurface | deformation | Mathematics - Algebraic Geometry
Journal Article
Nagoya mathematical journal, ISSN 0027-7630, 03/2012, Volume 205, pp. 25 - 65
We establish here several “invariance of plurigenera type” theorems for twisted pluricanonical forms and metrics of adjoint ℝ-bundles. 
INVARIANCE | BUNDLE | MATHEMATICS | ALGEBRAIC-VARIETIES | THEOREM | DEFORMATIONS | OHSAWA-TAKEGOSHI | GENERAL TYPE | PLURIGENERA | 32Q15 | 14E99 | 14D07 | Matematik | Mathematics
Journal Article
Letters in mathematical physics, ISSN 1573-0530, 2018, Volume 108, Issue 9, pp. 2055 - 2097
We describe some $$L_{\infty }$$ L∞ model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated... 
Geometry | 32G20 | 14D07 | Theoretical, Mathematical and Computational Physics | Complex Systems | Group Theory and Generalizations | Yukawa algebra | L-infinity algebras | 13D10 | Physics | Formal period maps | LIE-ALGEBRAS | SPACE | COHOMOLOGY | DEFORMATIONS | CONSTRUCTION | MANIFOLDS | PHYSICS, MATHEMATICAL | HOMOTOPY-THEORY | GEOMETRY | Analysis | Algebra
Journal Article
Science China Mathematics, ISSN 1674-7283, 1/2019, Volume 62, Issue 1, pp. 171 - 184
For a one parameter family of Calabi-Yau threefolds, Green et al. (2009) expressed the total singularities in terms of the degrees of Hodge bundles and Euler... 
14D07 | 55R55 | BCOV invariants | singularities | 14C40 | Arakelov inequalities | Mathematics | Applications of Mathematics | Calabi-Yau manifolds | 14D06 | 14J32 | MATHEMATICS, APPLIED | HOLOMORPHIC DETERMINANT BUNDLES | QUILLEN METRICS | MATHEMATICS | WEIL-PETERSSON GEOMETRY | R-TORSION | ANALYTIC-TORSION | MODULI SPACE | ALGEBRAIC-MANIFOLDS
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2016, Volume 165, Issue 4, pp. 661 - 721
We study certain spaces of nilpotent orbits in Hodge domains, and we treat a number of examples. More precisely, we compute the Mumford-Tate group of the limit... 
MATHEMATICS | VARIETIES | LOGARITHMIC DEFORMATIONS | MANIFOLDS | MIXED HODGE-STRUCTURES | FAMILY | 32G20 | 17B45 | Mumford–Tate domain | 14D07 | Mumford–Tate group | limit mixed Hodge structure | CM abelian variety | 14M17 | 32M10 | boundary component | Kato–Usui space | 20G99
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 2/2014, Volume 276, Issue 1, pp. 543 - 555
We get a new inequality on the Hodge number $$h^{1,1}(S)$$ h 1 , 1 ( S ) of fibred algebraic complex surfaces $$S$$ S , which is a generalization of an... 
Hodge number | Arakelov inequality | Singular fiber | 14D07 | 14C30 | Mathematics, general | Mathematics | 14D06 | Non-compact Jacobian
Journal Article
Mathematische Annalen, ISSN 0025-5831, 10/2012, Volume 354, Issue 2, pp. 727 - 763
For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic... 
Mathematics, general | 14F10 | Mathematics | 14D07 | 32C38 | HODGE-MODULES | MATHEMATICS | RATIONAL INTEGRALS | PERIODS
Journal Article
Compositio mathematica, ISSN 0010-437X, 07/2018, Volume 154, Issue 7, pp. 1534 - 1570
Let $X$ be a smooth complex projective variety with basepoint $x$ . We prove that every rigid integral irreducible representation... 
fundamental group | complex variation of Hodge structure | rigid representation | complex varieties | MATHEMATICS | BUNDLES | LEFSCHETZ THEOREMS | INEQUALITY | VARIETIES | CONJECTURE | Mathematics - Algebraic Geometry | Algebraic Geometry | Mathematics
Journal Article
Letters in mathematical physics, ISSN 1573-0530, 2013, Volume 103, Issue 9, pp. 933 - 1007
We discuss the structure of renormalized Feynman rules. Regarding them as maps from the Hopf algebra of Feynman graphs to $${\mathbb{C}}$$ originating from the... 
14D07 | Theoretical, Mathematical and Computational Physics | parametric renormalization | Statistical Physics, Dynamical Systems and Complexity | Physics | 81T18 | Geometry | Feynman rules | 81T15 | kinematics of scattering amplitudes | 81Q30 | Group Theory and Generalizations | Hopf algebras | PHYSICS, MATHEMATICAL | Analysis | Algebra
Journal Article
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