2 citations · 2 across the 23 of their papers we have counts for
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A note on period domains of Hodge structures
Mohammad Reza Rahmati
We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomol…
Mixed Hodge Structures on Generalized Theta Divisors and Graph Motives
Mohammad Reza Rahmati
This article studies the mixed Hodge structures that appear on the complements of generalized theta divisors inside generalized Jacobians of curves with modulus. For a smooth or no…
Higher Residue Pairing for -adic Isocrystals and the -adic Riemann--Hilbert Correspondence
Mohammad Reza Rahmati
We construct a canonical sesquilinear pairing on the relative crystalline cohomology of a smooth proper family of varieties over a complete discretely valued -adic field. Motiva…
Variation of Hodge Structure and Hodge modules
Mohammad Reza Rahmati
This text is an expository survey on the interplay between polarized variation of Hodge structure (PVHS) and the formalism of Hodge modules. We specifically review the extensions o…
Serre Intersection Multiplicity Conjecture and Hodge theory
Mohammad Reza Rahmati
We explain intersection multiplicity defined by J. P. Serre, in terms of the Poincare product in Hodge theory by a modification of the chern character map. We also discuss a formul…
Variation of Mixed Hodge Structure and Primitive elements
Mohammad Reza Rahmati
We study the asymptotic behaviour of polarization form in the variation of mixed Hodge structure associated to isolated hypersurface singularities. The contribution characterizes a…
Positivity of Hochster Theta
Mohammad Reza Rahmati
M. Hochster defines an invariant namely associated to two finitely generated module over a hyper-surface ring , where or , for…
A Hodge index for Grothendieck residue pairing
Mohammad Reza Rahmati
In this text we apply the methods of Hodge theory for isolated hypersurface singularities to define a signature for the Grothendieck residue pairing of these singularities.
On the mixed Hodge structure associated to hypersurface singularities
Mohammad Reza Rahmati
Let be a germ of hypersurface with isolated singularity. One can associate to a polarized variation of mixed Hodge structure o…