We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties satisfying an effective combina- torial property the Hodge conjecture holds. This gives a connection between the Oda conjecture and Hodge conjecture. We also give an explicit criterion which depends on the degree for very general hypersurfaces for the combinatorial condition to be verified
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e ...
We introduce $\ell$-Galois special subvarieties as an $\ell$-adic analog of the Hodge-theoretic noti...
AbstractFor projective varieties with a certain class of ‘mild’ isolated singularities and for proje...
We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties...
We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we stud...
This is the announcement of a conjecture on a Hodge locus for cubic hypersurfaces.Comment: With an a...
In this thesis we study toric hypersurfaces in the context of higher-dimensional algebraic geometry....
This thesis tackles different problems related to the connection between geometric and Hodge theoret...
We explicitly describe cohomology of complete intersec-tions in compact simplicial toric varieties. ...
These notes should be seen as a companion to [8], where thealgebraicity of the loci of Hodge classes...
The space of Hodge cycles of the general Prym variety is proved to be generated by its Neron-Severi ...
We combine Deligne's global invariant cycle theorem, and the algebraicity theorem of Cattani, Delign...
AbstractIn this paper for every p > 0 the universal family of the hypersurfaces of degree 2p and dim...
We introduce the notion of dR-absolutely special subvarieties in motivic variations of Hodge structu...
We generalize former results of Zuo and the first author showing some hyperbolicity properties of va...
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e ...
We introduce $\ell$-Galois special subvarieties as an $\ell$-adic analog of the Hodge-theoretic noti...
AbstractFor projective varieties with a certain class of ‘mild’ isolated singularities and for proje...
We show that for very general hypersurfaces in odd-dimensional simplicial projective toric varieties...
We establish the Hodge conjecture for some subvarieties of a class of toric varieties. First we stud...
This is the announcement of a conjecture on a Hodge locus for cubic hypersurfaces.Comment: With an a...
In this thesis we study toric hypersurfaces in the context of higher-dimensional algebraic geometry....
This thesis tackles different problems related to the connection between geometric and Hodge theoret...
We explicitly describe cohomology of complete intersec-tions in compact simplicial toric varieties. ...
These notes should be seen as a companion to [8], where thealgebraicity of the loci of Hodge classes...
The space of Hodge cycles of the general Prym variety is proved to be generated by its Neron-Severi ...
We combine Deligne's global invariant cycle theorem, and the algebraicity theorem of Cattani, Delign...
AbstractIn this paper for every p > 0 the universal family of the hypersurfaces of degree 2p and dim...
We introduce the notion of dR-absolutely special subvarieties in motivic variations of Hodge structu...
We generalize former results of Zuo and the first author showing some hyperbolicity properties of va...
We introduce the intersection cohomology module of a matroid and prove that it satisfies Poincar\'e ...
We introduce $\ell$-Galois special subvarieties as an $\ell$-adic analog of the Hodge-theoretic noti...
AbstractFor projective varieties with a certain class of ‘mild’ isolated singularities and for proje...
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