相关论文: On non-Archimedean curves omitting few components …

Let $D$ be a big integral divisor on a smooth projective surface $X$. In this paper, we study Noether-type inequalities for $D$. The key ingredient is the introduction of a numerical invariant $\mathfrak{e}(D)$, which depends only on the…

This note is the sequel to [A note on secondary K-theory. Algebra and Number Theory 10 (2016), no. 4, 887-906]. Making use of the recent theory of noncommutative motives, we prove that the canonical map from the derived Brauer group to the…

Let k be a number field and X a smooth projective k-variety. In this paper, we study the information obtainable from descent via torsors under finite k-group schemes on the location of the k-rational points on X within the adelic points.…

In this paper, we study quasi post-critically finite degenerations for rational maps. We construct limits for such degenerations as geometrically finite rational maps on a finite tree of Riemann spheres. We prove the boundedness for such…

In this paper we construct $n$-valued maps on $k$-dimensional tori, where $n,k\geq 2$, that are not homotopic to affine $n$-valued maps. This is in high contrast with the single valued case, where any such map is homotopic to an affine…

Let $\mathfrak D$ be a residually finite Dedekind domain, $a\in \mathfrak D$ be a nonzero element and $\mathfrak n$ be a nonzero ideal of $\mathfrak D$. In this paper we describe the dynamics of the map $x\mapsto ax$ over the quotient ring…

We give a general criterion for Zariski degeneration of integral points in the complement of a divisor $D$ with $n$ components in a variety of dimension $n$ defined over $\mathbb{Q}$ or over a quadratic imaginary field. The key condition is…

Let $X$ be a smooth projective algebraic variety over a number field $k$ and $P$ in $X(k)$. In 2007, the second author conjectured that, in a precise sense, if rational points on $X$ are dense enough, then the best rational approximations…

We consider the locus of irreducible nonsingular rational curves of degree d Pn, n>2, meeting a generic collection of linear subspaces. When this locus is 0 (resp 1)- dimensional, we compute (recursively) its degree (resp. geometric genus).…

The purpose of this article is twofold. On the one hand, we prove asymptotic formulas for the quantitative distribution of rational points on any smooth non-split projective quadratic surface. We obtain the optimal error term for the real…

We establish a non-Archimedean analogue of Koksma's theorem. For a local field F of characteristic zero, we prove that the sequence ([{\alpha}x^n]) is uniformly distributed in the valuation ring O for almost every x with |x|_p>1. In the…

Physically meaningful periodic solutions to certain integrable partial differential equations are given in terms of multi-dimensional theta functions associated to real Riemann surfaces. Typical analytical problems in the numerical…

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\sl generic} hypersuface…

We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can…

For each positive integer k, we describe a map f from the complex plane to a suitable non-complete complex locally convex space such that f is k times continuously complex differentiable but not k+1 times, and hence not complex analytic. We…

In this paper, we study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. We show that a complete noncompact manifold with asymptoticaly nonnegative Ricci curvature and sectional…

Let T -> S be a finite flat morphism of degree two between regular integral schemes of dimension at most two (and with 2 invertible), having regular branch divisor D. We establish a bijection between Azumaya quaternion algebras on T and…

We propose a linear version of the weighted bounded negativity conjecture. It considers a smooth projective surface $X$ over an algebraically closed field of characteristic zero and predicts the existence of a common lower bound on…

The cones of divisors and curves defined by various positivity conditions on a smooth projective variety have been the subject of a great deal of work in algebraic geometry, and by now they are quite well understood. However the analogous…

We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into…