Related papers: Iitaka's $C_{n,m}$ conjecture for 3-folds over fin…
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…
We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…
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.
In this short note we prove the Iitaka C_nm conjecture for algebraic fiber spaces over surfaces
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…
We prove the following results for projective klt pairs of dimension $3$ over an algebraically closed field of char $p>5$: the cone theorem, the base point free theorem, the contraction theorem, finiteness of minimal models, termination…
We prove that the Iitaka conjecture $C_{n,m}$ for algebraic fibre spaces holds up to dimension 6, that is, when $n\le 6$.
The Tate conjecture for squares of K3 surfaces over finite fields was recently proved by Ito-Ito-Koshikawa. We give a more geometric proof when the characteristic is at least 5. The main idea is to use twisted derived equivalences between…
We prove some finiteness results on the movable cone for mildly singular 3-folds with semiample anticanonical bundle, giving some evidence for the Morrison--Kawamata cone conjecture for klt pairs.
In this paper, we give a new proof of the foundational result, due to S. Cutkosky, on the existence of a monomialisation of a morphism from a 3-fold to a surface. Our proof brings to the fore the notion of log-Fitting ideals, and requires…
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 an analogue of Fujino and Mori's ``bounding the denominators'' in the log canonical bundle formula (see also Prokhorov and Shokurov) for Kawamata log terminal pairs of relative dimension one. As an application we prove that for a…
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 prove Simon's conjecture for 3-manifolds.
We investigate the moduli theory of Calabi--Yau threefolds, and using Griffiths' work on the period map, we derive some finiteness results. In particular, we confirm a prediction of Morrison's Cone Conjecture.
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
We give applications of integral canonical models of orthogonal Shimura varieties and the Kuga-Satake morphism to the arithmetic of K3 surfaces over finite fields. We prove every K3 surface of finite height over a finite field admits a…
Let $(M,g)$ be a complete $(n+1)$-dimensional Riemannian manifold with $2\leq n\leq 6$. Our main theorem generalizes the solution of S.-T. Yau's conjecture on the abundance of minimal surfaces and builds on a result of M. Gromov. Suppose…
In this paper, we show that Fujita's basepoint-freeness conjecture for projective quasi-log canonical singularities holds true in dimension three. Immediately, we prove Fujita-type basepoint-freeness for projective semi-log canonical…
We establish the real integral Hodge conjecture for 1-cycles on various classes of uniruled threefolds (conic bundles, Fano threefolds with no real point, some del Pezzo fibrations) and on conic bundles over higher-dimensional bases which…