activity
20242026
collaborators

7 papers

math.AG2026

Kodaira dimension of algebraic fiber spaces over threefolds : Part 1

Houari Benammar Ammar

We study the behavior of the Kodaira dimension of algebraic fiber spaces over threefolds. We prove some cases of the Iitaka Conjecture , including certain situations where…

math.AG2025

Note on Iitaka Conjecture

Houari Benammar Ammar

Let \( f: X \to Y \) be an algebraic fiber space, where \( X \) and \( Y \) are smooth projective varieties of dimensions \( n \) and \( m \), respectively. In \cite{Caopaun}, Cao…

math.AG2025

An Inductive Approach to Basepoint-Freeness of Adjoint Series on Irregular Varietiess

Houari Benammar Ammar

In this paper, we show how to prove the basepoint-freeness for linear systems on irregular varieties inductively. For instance, we prove that Fujita's conjecture holds for irregula…

math.AG2025

Trigonal Canonically Fibered Surfaces

Houari Benammar Ammar, Xi Chen, Nathan Grieve

We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a mu…

math.AG2025

Remarks on the Direct Image Sheaf of Logarithmic Pluricanonical Bundles and the Non-Vanishing Conjecture

Houari Benammar Ammar

By applying the Chen-Jiang decomposition, we prove that the non-vanishing conjecture holds for an lc pair \((X, Δ)\), where \(X\) is an irregular variety, provided it holds for lo…

math.AG2024

Delta-invariant for projective bundles over a curve and K-semistability

Houari Benammar Ammar, Louis Massonnet, Chenxi Yin

Consider a vector bundle over a smooth curve . We compute the -invariant of all ample (-) line bundles on when is strictly Mumford semist…