相关论文: Singularities of divisors of low degree on abelian…

We give some easy necessary and sufficient criteria for twists of abelian varieties by Artin representations to be simple.

We describe a sufficient condition for the localization functor to be a categorical equivalence. Using this result we explain how to simplify the test for projectivity. This leads to a description of the strictly simple algebras which are…

Let $A$ be an abelian variety over ${\bf C}$ of dimension $n$ and $\pi\colon {\bf C}^n \rightarrow A$ be the complex uniformisation. Let $X$ be an unbounded subset of ${\bf C}^n$ definable in a suitable o-minimal structure. We give a…

The singularities of theta divisors have played an important role in the study of algebraic varieties. This paper surveys some of the recent progress in this subject, using as motivation some well known results, especially those for…

We show that a principally polarized abelian variety over a field $k$ is, as an abelian variety, a direct summand of a product of Jacobians of curves which contain a $k$-point if and only if the polarization and the minimal class are both…

This paper proves the following converse to a theorem of Mumford: Let $A$ be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point…

In a previous paper we showed that for every polarization on an abelian variety there is a dual polarization on the dual abelian variety. In this note we extend this notion of duality to families of polarized abelian varieties. As a main…

We solve a case of the Abelian Exponential-Algebraic Closedness Conjecture, a conjecture due to Bays and Kirby, building on work of Zilber, which predicts sufficient conditions for systems of equations involving algebraic operations and the…

We introduce a simplified version of the Grothendieck group of algebraic varieties and use it to show that birational types specialize in families with mild singularities of the central fiber.

In this paper we study holomorphic foliations on $\mathbb{P}^2$ with only one singular point. If the singularity has algebraic multiplicity one, we prove that the foliation has no invariant algebraic curve. We also present several examples…

We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary isogeny classes.

We prove that the log canonical threshold of the base ideal of a complete linear system on a complex abelian variety is $\ge 1$, and equality holds if and only if the base locus has divisorial components. Consequently the same assertions…

We study in this paper some criterions to get polarized morphisms between abelian varieties. We deduce explicit dynamical systems with particular intersection properties.

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…

Given a principally polarized abelian variety $(A,\Theta)$, we give a characterization of all elliptic curves that lie on $A$ in terms of intersection numbers of divisor classes in its N\'eron-Severi group.

Let $X \to S$ be a minimal abelian fibration of relative dimension $n$ over a curve. We classify all possible singular fibers $X_s$ having $(n-1)$-dimensional ``abelian variety parts''. This generalizes Kodaira's work on elliptic…

In this note we study the geometry of principally polarized abelian varieties (ppavs) with a vanishing theta-null (i.e. with a singular point of order two and even multiplicity lying on the theta divisor). We describe the locus within the…

We give a necessary and sufficient condition for a representation of the fundamental group of a closed surface of genus at least 2 to $\mathbb C$ to be the holonomy of a translation surface with a prescribed list of conical singularities.…

Let F be a real quadratic field, and let R be an order in F. Suppose given a polarized abelian surface (A,\lambda) defined over a number field k with a symmetric action of R defined over k. This paper considers varying A within the…

We discuss Galois properties of points of prime order on an abelian variety that imply the simplicity of its endomorphism algebra. Applications to hyperelliptic jacobians are given. In particular, we improve some of our earlier results.