8 papers
Log Canonical Counterexamples to the Chen--Jiang Decomposition
Houari Benammar Ammar
We construct a projective log-smooth surface pair and a morphism to an elliptic curve such that $f_*\OO_X(K_X+Δ)$ is Atiyah's indecomposable rank-two bundle $F_2…
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…
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…
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…
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 low…
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 semista…
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…
Slope inequality for an arbitrary divisor
Houari Benammar Ammar
Let be a surjective morphism with connected fibers from a smooth complex projective surface to a smooth complex projective curve with general fiber…