arXiv subjects

Houari Benammar Ammar

Publications and source records attributed to Houari Benammar Ammar.

8 recordsLinked to original sources

arXiv2026

Log Canonical Counterexamples to the Chen--Jiang Decomposition

We construct a projective log-smooth surface pair $(X,Δ)$ and a morphism $f:X\to E$ to an elliptic curve such that $f_*\OO_X(K_X+Δ)$ is Atiyah's indecomposable rank-two bundle $F_2$ of degree zero. This gives a negative answer to Question 3.4 of Jiang \cite{Jiang}. We also construct a log canonical pair $(X,Δ)$ and a morphism $f$ to an abelian surface such that $f_*\OO_X(m(K_X+Δ))$ does not admit a Chen--Jiang decomposition for any integer $m\ge2$. Products yield counterexamples in every higher direct image degree and over abelian bases of arbitrary positive dimension.

math.AG↗

arXiv2026

Kodaira dimension of algebraic fiber spaces over threefolds : Part 1

We study the behavior of the Kodaira dimension of algebraic fiber spaces over threefolds. We prove some cases of the Iitaka Conjecture $C_{n,3}$, including certain situations where the base variety is a Calabi--Yau threefold.

math.AG↗

arXiv2025

Note on Iitaka Conjecture $C_{n,m}$

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 and Păun proved $ C_{n,m} $ when $ Y $ has maximal Albanese dimension. In this paper, we prove $ C_{n,m} $ in the case where the Albanese dimension $α(Y)$ of $ Y $ satisfies $ α(Y) \geq m-2 $.

math.AG↗

arXiv2025

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

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 irregular varieties of dimension $\mathnormal{n}$ with a nef anticanonical bundle assuming it holds for lower-dimensional varieties and under mild conditions.

math.AG↗

arXiv2025

Trigonal Canonically Fibered Surfaces

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 much better bound on the geometric genus of the surface. Also we apply the same argument to canonically fibered surfaces of relative genus 3 and 4 to obtain some Noether-type inequalities for these surfaces.

math.AG↗

arXiv2025

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

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 lower-dimensional varieties. In the second part, we extend the Catanese-Fujita-Kawamata decomposition to the klt case $(X, Δ)$, which leads to the existence of sections of $K_X + Δ$ in certain situations.

math.AG↗

arXiv2024

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

Consider $E$ a vector bundle over a smooth curve $C$. We compute the $δ$-invariant of all ample ($\mathbb{Q}$-) line bundles on $\mathbb{P}(E)$ when $E$ is strictly Mumford semistable. We also investigate the case when one assumes that the Harder-Narasimhan filtration of $E$ has only one step.

math.AG↗

arXiv2024

Slope inequality for an arbitrary divisor

Let $f: S \longrightarrow C$ be a surjective morphism with connected fibers from a smooth complex projective surface $S$ to a smooth complex projective curve $C$ with general fiber $F$. In this paper, we develop a more general version of the slope inequality for data $(D, \mathcal{F})$, where $D$ is an arbitrary relatively effective divisor on $S$ and $\mathcal{F}$ is a locally free sub-sheaf of $f_{*}\mathcal{O}_{S}(D)$. We see how the speciality of $D$, restricted to the general fiber, plays a role in the results. Moreover, we compute some natural examples and provide applications.

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