Mixed Hodge-Riemann bilinear relations and m-positivity
Sign Up to like & getrecommendations! Published in 2018 at "Science China Mathematics"
DOI: 10.1007/s11425-020-1704-2
Abstract: Motivated by our previous work on Hodge-index type theorems, we give a form of mixed Hodge-Riemann bilinear relation by using the notion of m -positivity, whose proof is an adaptation of the works of Timorin… read more here.
Keywords: positivity; mixed hodge; hodge riemann; riemann bilinear ... See more keywords
TheE3∕Z3orbifold, mirror symmetry, and Hodge structures of Calabi–Yau type
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2018.12.020
Abstract: Starting from the K\"ahler moduli space of the rigid orbifold Z=E^3/\mathbb{Z}_3 one would expect for the cohomology of the generalized mirror to be a Hodge structure of Calabi-Yau type (1,9,9,1). We show that such a… read more here.
Keywords: mirror; calabi yau; hodge; yau type ... See more keywords
On Hodge polynomials for nonalgebraic complex manifolds
Sign Up to like & getrecommendations! Published in 2025 at "Proceedings of the National Academy of Sciences of the United States of America"
DOI: 10.1073/pnas.2415722122
Abstract: Significance Hodge theory connects the geometry of algebraic varieties to their topological properties via the Hodge decomposition and Hodge diamond. It has been central to developments in mirror symmetry, algebraic cycles, and motives. This paper… read more here.
Keywords: hodge polynomials; polynomials nonalgebraic; geometry; complex manifolds ... See more keywords
A Note on 1-Motives
Sign Up to like & getrecommendations! Published in 2019 at "International Mathematics Research Notices"
DOI: 10.1093/imrn/rny295
Abstract: We prove that for $1$-motives defined over an algebraically closed subfield of $\mathbf{C}$, viewed as Nori motives, the motivic Galois group coincides with the Mumford–Tate group. In particular, the Hodge realization of the Tannakian category… read more here.
Keywords: hodge; note motives;
Locational Detection of False Data Injection Attacks in the Edge Space via Hodge Graph Neural Network for Smart Grids
Sign Up to like & getrecommendations! Published in 2024 at "IEEE Transactions on Smart Grid"
DOI: 10.1109/tsg.2024.3389948
Abstract: Recently, the emerging False Data Injection Attacks (FDIAs), one of the major cybersecurity threats, have been severely threatening smart grids, since FDIAs could bypass conventional bad data detectors to disrupt power system operations. To maintain… read more here.
Keywords: locational detection; hodge; graph; edge space ... See more keywords
Hodge Decomposition of Conformal Vector Fields on a Riemannian Manifold and Its Applications
Sign Up to like & getrecommendations! Published in 2024 at "Mathematics"
DOI: 10.3390/math12172628
Abstract: For a compact Riemannian m-manifold (Mm,g),m>1, endowed with a nontrivial conformal vector field ζ with a conformal factor σ, there is an associated skew-symmetric tensor φ called the associated tensor, and also, ζ admits the… read more here.
Keywords: vector; tensor; riemannian manifold; conformal vector ... See more keywords
2D discrete Hodge-Dirac operator on the torus
Sign Up to like & getrecommendations! Published in 2022 at "Symmetry"
DOI: 10.3390/sym14081556
Abstract: We discuss a discretization of the de Rham–Hodge theory in the two-dimensional case based on a discrete exterior calculus framework. We present discrete analogues of the Hodge–Dirac and Laplace operators in which key geometric aspects… read more here.
Keywords: dirac operator; operator torus; hodge; hodge dirac ... See more keywords
Variation of Mixed Hodge Structures Associated to an Equisingular One-dimensional Family of Calabi-Yau Threefolds
Sign Up to like & getrecommendations! Published in 2020 at "Canadian Journal of Mathematics"
DOI: 10.4153/s0008414x20000024
Abstract: Abstract We study the variations of mixed Hodge structures (VMHS) associated with a pencil ${\mathcal{X}}$ of equisingular hypersurfaces of degree $d$ in $\mathbb{P}^{4}$ with only ordinary double points as singularities, as well as the variations… read more here.
Keywords: hodge; hodge structures; variation mixed; mixed hodge ... See more keywords