Mixed Hodge-Riemann bilinear relations and m-positivity
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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
A Note on 1-Motives
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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;
2D discrete Hodge-Dirac operator on the torus
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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
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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