6 papers
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…
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…
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…
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{…
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…
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…