Related papers: Characterization of Abelian Varieties

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…

We give an explicit characterization of all principally polarized abelian varieties $(A,\Theta)$ such that there is a finite subgroup of automorphisms $G$ of $A$ that preserve the numerical class of $\Theta$, and such that the quotient…

We study canonical and pluricanonical maps of varieties isogenous to a product of curves, i.e., quotients of the form $X = (C_1 \times \dots \times C_n)/G$ with $g(C_i)\ge 2$ and $G$ acting freely. For this purpose, we provide a technical…

Let $(X,B)$ be a complex projective klt pair, and let $f\colon X\to Z$ be a surjective morphism onto a normal projective variety with maximal albanese dimension such that $K_X+B$ is relatively big over $Z$. We show that such pairs have good…

We prove (by a case-by-case analysis) a conjecture of Bernstein/Schwarzman to the effect that quotients of abelian varieties by suitable actions of (complex) reflection groups are weighted projective spaces, and show that this remains true…

Chevalley's theorem states that every smooth connected algebraic group over a perfect field is an extension of an abelian variety by a smooth connected affine group. That fails when the base field is not perfect. We define a pseudo-abelian…

Let $A$ be an abelian variety and $G$ a finite group of automorphisms of $A$ fixing the origin such that $A/G$ is smooth. The quotient $A/G$ can be seen as a fibration over an abelian variety whose fibers are isomorphic to a product of…

We give a complete classification of smooth quotients of abelian varieties by finite groups that fix the origin. In the particular case where the action of the group $G$ on the tangent space at the origin of the abelian variety $A$ is…

A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…

In this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic $p>0$ is isogenous to another one defined over a finite field. We also show that the category of…

A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if $X$ is a projective variety over an algebraically closed field of characteristic zero which admits a global algebraic…

We show that the vector bundle associated to a smooth projective connected finite covering of a simple complex abelian variety is ample (under a simple necessary condition). This result is obtained by showing that this bundle is M-regular…

Let $X/\mathbb{F}_{q}$ be a smooth geometrically connected variety. Inspired by work of Corlette-Simpson over $\mathbb{C}$, we formulate a conjecture that absolutely irreducible rank 2 local systems with infinite monodromy on $X$ come from…

We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is…

Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number fields to prove that if X and Y are…

We prove that a 1-dimnl family of abelian varieties with an ample sheaf defining principal polarization can be canonically compactified (after a finite base change) to a projective family with an ample sheaf. We show that the central fiber…

This paper gives a conjectural characterization of those elliptic curves over the field of complex numbers which "should" be covered by standard modular curves. The elliptic curves in question all have algebraic j-invariant, so they can be…

We classify varieties with $P_3(X)=4$ and $q(X)=\dim (X)$.

We shall show how to decompose, by functorial and canonical fibrations, arbitrary $n$-dimensional complex projective {Although the geometric results apply to compact K\" ahler manifolds without change, we consider here for simplicity this…

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…