2 citations · 2 across the 23 of their papers we have counts for
27 papers
Calabi-Yau attractor varieties and degeneration of Hodge structure
Mohammad Reza Rahmati
We study the structure of string theory flux compactification for a general family of elliptic CY 3-folds. We investigate the locus of the attractor points of the flux compactifica…
A question on generalization of partition functions of CY 3-folds in String Theory
Mohammad Reza Rahmati
This is an expositoray article on the topological string partition function promoting an extension of the partition function of open Gromov-Witten theory of CY 3-folds defined by t…
Tropical Normal Functions -- Higher Abel-Jacobi Invariants of Tropical cycles
Mohammad Reza Rahmati
We consider the variation of tropical Hodge structure (TVHS) associated to families of tropical varieties. The family of the tropical intermediate Jacobians of the associated tropi…
Hodge-Arakelov inequalities for family of surfaces fibered by curves
Mohammad Reza Rahmati
The Hodge numerical invariants of a variation of Hodge structure over a smooth quas--projective variety are a measure of complexity for the global twisting of the limit mixed Hodge…
Invariant Jet differentials and Asymptotic Serre duality
Mohammad Reza Rahmati
We generalize the main result of Demailly \cite{D2} for the bundles of jet differentials of order and weighted degree to the bundles of t…
Finite Generation and Structure of Invariant Jets under Non-Reductive Reparametrization
Mohammad Reza Rahmati
We study invariant jet differentials in the framework of complex hyperbolicity, focusing on the algebra of invariants for the non--reductive reparametrization group $G_k = \mathbb{…
Geometry of Weighted Homogeneous Spaces
Mohammad Reza Rahmati, Gerardo Flores
In this paper, we define the weighted homogeneous space (WHS), denoted by where is weight function defined on the set of simple roots of , by an element…
Schur-Weyl Duality and Higher Abel-Jacobi Invariants for Tautological Cycles in
Mohammad Reza Rahmati
This article investigates the Hodge theory of the moduli space of genus curves with marked points, establishing new connections between Schur-Weyl duality for $\mathfrak{sp…
Fock Space of Level infinity and Characters of Vertex Operators
Mohammad Reza Rahmati, Gerardo Flores
We present an extension of the trace of a vertex operator and explain a representation-theoretic interpretation of the trace. Specifically, we consider a twist of the vertex operat…
Morse cohomology estimates for jet differential operators
Jean-Pierre Demailly, Mohammad Reza Rahmati
We provide detailed holomorphic Morse estimates for the cohomology of sheaves of jet differentials and their dual sheaves. These estimates apply on arbitrary directed varieties, an…
Curvature of Metrics on Semple Jet bundles
Mohammad Reza Rahmati
We discuss the Morse estimates for the curvature of several metrics on Semple weighted projective bundle over a projective variety. Following Demailly works on holomorphic Morse in…
A note on the ring of invariant jet differentials
Mohammad Reza Rahmati
In this article we briefly discuss the finite generation of fiber rings of invariant k-jets of holomorphic curves in a complex projective manifold, using differential Galois theory…
A note on asymptotic Serre duality for jet differentials
Mohammad Reza Rahmati
We formulate and prove the existence of an asymptotic duality along the fibers of the Green-Griffiths jet bundles over projective manifolds. The existence of global sections for th…
Vertex algebras and Hodge structures
Mohammad Reza Rahmati
We compare the context of Hodge structures with that of vertex algebras of conformal field theory. Vertex algebras appear as the highest weight representations of infinite dimensio…
Nilpotent orbit theorem in -adic Hodge theory
Mohammad Reza Rahmati, Gerardo Flores
We state and prove three orbit theorems on the period domains for the -adic Hodge structure analogous to the complex case. We shall consider the variation of de Rham (resp. étal…
On Serre Intersection Multiplicity Conjecture
Mohammad Reza Rahmati
In this short note, we expose some of the works on Serre intersection multiplicity conjecture. I provide a proof of the vanishing of Serre intersection multiplicity in non-proper i…
de Rham Cohomology of Period Domains
Mohammad Reza Rahmati
This is a review article discussing the de Rham cohomology of period domains of Hodge structures. We explain it as the de Rham cohomology of differentiable stacks as of a moduli sp…
Toroidal Compactifications and Stacky Cohomology of Mumford--Tate Domains
Mohammad Reza Rahmati
Mumford--Tate domains parametrize polarized Hodge structures with fixed Mumford--Tate group and play a central role in the geometry of period maps. Their degenerations are governed…
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…