7 papers
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…
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…
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 \((X, Î)\), where \(X\) is an irregular variety, provided it holds for lo…
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…