Related papers: Iitaka conjecture $C_{n,m}$ in dimension six

The main purpose of this paper is to prove the Iitaka conjecture $C_{n,m}$ on the assumption that the sufficiently general fibers have maximal Albanese dimension.

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 P\u{a}un proved \( C_{n,m} \) when \( Y \) has maximal…

In this article, we will prove the Generalized Nonvanishing Conjecture holds for threefolds with either $\kappa>0$ or $q>0$. As a result, we can prove the Iitaka conjecture $C_{n,m}$ holds for $n=7$ if the source space has non-negative…

In this short note we prove the Iitaka C_nm conjecture for algebraic fiber spaces over surfaces

We prove Iitaka's $C_{n,m}$ conjecture for $3$-folds over the algebraic closure of finite fields. Along the way we prove some results on the birational geometry of log surfaces over nonclosed fields and apply these to existence of relative…

In this short article we provide a proof of the Iitaka conjecture for algebraic fiber spaces over abelian varieties.

In this paper, we prove that for a fibration $f:X\to Z$ from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ with $\mathrm{char} k =p >5$, if the geometric generic fiber $X_{\overline\eta}$ is…

By applying the positivity theorem of direct images and a pluricanonical version of the structure theorem on the cohomology jumping loci \`a la Green-Lazarsfeld-Simpson, we show that the klt K\"ahler version of the Iitaka conjecture…

We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that the conjecture on the existence of complements implies the…

We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.

We show that the M-canonical map of an n-dimensional complex projective manifold X of Kodaira dimension two is birational to an Iitaka fibration for a computable positive integer M. M depends on the index b of a general fibre F of the…

In this paper, by running MMP and considering the anti-canonical fibration, we prove the Morrison-Kawamata cone conjecture for klt Calabi-Yau pairs $(X,\Delta)$ such that $\dim X$ is at most $4$, and the Iitaka dimension $\kappa(X,-K_X)$ is…

We prove Manin's conjecture over imaginary quadratic number fields for a cubic surface with a singularity of type E_6.

The purpose of this paper is to establish a subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As applications, we obtain a product formula of the restricted canonical volumes for algebraic fiber spaces and a sufficient…

Let $f:X\to Y$ be a fibration from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p >5$. We prove that if the generic fiber $X_{\eta}$ has big canonical divisor…

We give a proof of Iitaka's Conjecture C_{2,1} using only elementary methods from algebraic geometry. The main point is that, given a non-isotrivial and relatively minimal family f : X \to B, where X is a surface and B is a curve, both…

We prove the effectiveness of the log Iitaka fibration in Kodaira codimension two for varieties of dimension$\le 4$. In particular, we finish the proof of effective log Iitaka fibration in dimension two. Also, we show that for the log…

We establish the volume conjecture for (m,2)-cables of the figure 8 knot, when m is odd. For (m,2)-cables of general knots where m is even, we show that the limit in the volume conjecture depends on the parity of the color (of the Kashaev…

Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve,…

We prove that for any smooth complex projective threefold of Kodaira dimension one, the $m$-th pluricanonical map is birational to the Iitaka fibration for every $m\geq5868$ and divisible by $12$.