Related papers: On maximal Albanese dimensional varieties

Since Poonen's construction of a variety $X$ defined over a number field $k$ for which $X(k)$ is empty and the \'etale Brauer--Manin set $X(\mathbf{A}_k)^\text{Br,et}$ is not, several other examples of smooth, projective varieties have been…

In this article, we introduce a new approach to show the existence and smoothing of simple normal crossing varieties in a given projective space. Our approach relates the above to the existence of nowhere reduced schemes called ribbons and…

We prove that in the varieties where every compact congruence is a factor congruence and every nontrivial algebra contains a minimal subalgebra, a finitely presented algebra is projective if and only if it has every minimal algebra as its…

We show that if X is a nonsingular projective variety of general type over an algebraically closed field k of positive characteristic and X has maximal Albanese dimension and the Albanese map is separable, then |4K_X| induces a birational…

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.

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo $p^2$ - we expect that such varieties, after a finite \'etale cover, admit a toric fibration over…

We study abelian varieties $A$ with multiplication by a totally indefinite quaternion algebra over a totally real number field and give a criterion for the existence of principal polarizations on them in pure arithmetic terms. Moreover, we…

We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.

We show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under monomial maps with finite fibers. The maximum likelihood estimator corresponding to such a variety is…

We prove that every smooth subelliptic variety admits a surjective morphism from an affine space. This result gives partial answers to the questions of Arzhantsev and Forstneri\v{c}. As an application, we characterize open images of…

In this note we show that any supersingular abelian variety is isogenous to a superspecial abelian variety without increasing field extensions. The proof uses minimal isogenies and the Galois descent. We then construct a superspecial…

We construct klt projective varieties with ample canonical class and the smallest known volume. We also find exceptional klt Fano varieties with the smallest known anticanonical volume. We conjecture that our examples have the smallest…

After a historical discussion of classical uniformisation results for Riemann surfaces, of problems appearing in higher dimensions, and of uniformisation results for projective manifolds with trivial or ample canonical bundle, we introduce…

This paper concerns the construction of minimal varieties with small canonical volumes. The first part devotes to establishing an effective nefness criterion for the canonical divisor of a weighted blow-up over a weighted hypersurface, from…

We give new examples of algebraic integral cohomology classes on smooth projective complex varieties that are not integral linear combinations of classes of smooth subvarieties. Some of our examples have dimension 6, the lowest possible.…

Let $k$ be an algebraically closed field of characteristic $p>0$. We give a birational characterization of ordinary abelian varieties over $k$: a smooth projective variety $X$ is birational to an ordinary abelian variety if and only if…

We prove the invariance of plurigenera under smooth projective deformations of varieties with nonnegative Kodaira dimensions.

Let S be a minimal complex surface of general type and of maximal Albanese dimension; by the Severi inequality one has $K^2_S\geq 4\chi(\mathcal O_S)$. We prove that the equality $K^2_S=4\chi(\mathcal O_S)$ holds if and only if $q(S):=…

We define partially ample subvarieties of projective varieties, generalizing Ottem's work on ample subvarieties, and show their ubiquity. As an application, we obtain a connectedness result for pre-images of subvarieties by morphisms,…

We show that the epimorphism problem is solvable for targets that are virtually cyclic or a product of an Abelian group and a finite group.