Related papers: Almost non-degenerate abelian fibrations

We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely…

We introduce a relaxation of stability, called almost sure stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a non-standard finite group. We show that almost sure stability satisfies a stationarity principle…

We provide examples of finite non-abelian groups acting on non-trivial Severi-Brauer surfaces.

In this paper, we introduce the notion of abelian endoregular modules as those modules whose endomorphism rings are abelian von Neumann regular. We characterize an abelian endoregular module $M$ in terms of its $M$-generated submodules. We…

We study the existence of Milnor fibration on a big enough sphere at infinity for a mixed polynomial $f: \bR^{2n} \to \bR^2$. By using strong non-degeneracy condition, we prove a counterpart of N\'emethi and Zaharia's fibration theorem. In…

By using non-positively curved cubings of prime alternating link exteriors, we prove that certain ideal triangulations of their complements, derived from reduced alternating diagrams, are non-degenerate, in the sense that none of the edges…

We prove asymptotics for the proportion of fibres with a rational point in a conic bundle fibration. The basis of the fibration is a general hypersurface of low degree.

Recent developments on the uniformity of the number of rational points on curves and subvarieties in a moving abelian variety rely on the geometric concept of the degeneracy locus. The first-named author investigated the degeneracy locus in…

For every finite abelian group $G$, there are positive integers $n$ and $d$ such that $G$ is isomorphic to the multiplicative group of $d$-th powers of reduced residues modulo $n$.

A precise and testable modularity conjecture for rational abelian surfaces A with trivial endomorphisms, End_Q A = Z, is presented. It is consistent with our examples, our non-existence results and recent work of C. Poor and D. S. Yuen on…

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…

We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebra is semisimple.

We prove that the pull back of an ample line bundle by an almost holomorphic Lagrangian fibration is nef. As an application, we show birational semi rigidity of Lagrangian fibrations.

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such…

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.

We construct examples of elliptic fibrations of orbifold general type (in the sense of Campana) which have no etale covers dominating a variety of general type.

As an application of the theory of linear parabolic differential equations on noncompact Riemannian manifolds, developed in earlier papers, we prove a maximal regularity theorem for nonuniformly parabolic boundary value problems in…

We prove that for a non-isotrivial abelian scheme over a smooth curve, the genus of a generic sequence of multi-sections with small heights tends to infinity. As an application, we give a new proof of the uniform boundedness of…

Let X be a non singular projective surface. Given a semistable non isotrivial fibration f over a smooth rational curve with general fiber non hyperelliptic of genus g bigger than 3, we show that if the number s of singular fibers is 5, then…