相关论文: Sur la th\'eorie d'Ahlfors des surfaces
We study the distribution of algebraic points on K3 surfaces.
We give a proof of a phenomenon conjectured in our former article: "Beltrami forms, affine surfaces and the Schwarz-Christoffel formula: a worked out example of straightening". We also start an abstract discussion of the notion of limits of…
Multisummation provides a transparent description of Stokes matrices which is reviewed here together with some applications. Examples of moduli spaces for Stokes matrices are computed and discussed. A moduli space for a third Painlev\'e…
We study the strong solvability of the nonstationary Stokes problem with non-zero divergence in a bounded domain.
The purpose of this paper is to initiate Arakelov theory in a noncommutative setting. More precisely, we are concerned with noncommutative arithmetic surfaces. We introduce a version of arithmetic intersection theory on noncommutative…
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
We formulate a method for computing Stokes flow past a highly deformed sphere with arbitrarily defined surface velocity. The fundamental ingredient is an explicit extrapolation operator extending a velocity field from the surface of a…
We give a simple proof of the Riemann-Roch theorem for Deligne-Mumford stacks using the equivariant Riemann-Roch theorem and the localization theorem in equivariant K-theory together with some basic commutative algebra of Artin rings.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
We present some new Stokes' type theorems on complete non-compact manifolds that extend, in different directions, previous work by Gaffney and Karp and also the so called Kelvin-Nevanlinna-Royden criterion for (p-)parabolicity. Applications…
A proof based on the Chern-Gauss-Bonnet Theorem is given to Hopf Theorem concerning the degree of the Gauss map of a hypersurface in $\mathbb{R}^n$.
We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of M\"oller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in…
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
The main result of the paper is a boundedness for $n$-complements on algebraic surfaces. In addition, applications of this theorem to a classification of log Del Pezzo surfaces and of birational contractions for 3-folds are formulated.
We study the surface of Gauss double points associated to a very general quartic surface and the natural morphisms associated to it.
The paper contains a new proof of the theorem by Krieger which establishes the canonicity of the future cover of a sofic shift. In addition the paper describes a method to produce new canonical covers from a given one, resulting in…
We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-abelian version of Stokes' theorem.
We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.
We provide a simple proof of Pascal's Theorem on cyclic hexagons, as well as a generalization by M\"obius, using hyperbolic geometry.
The connection between the theory of permutation orbifolds, covering surfaces and uniformization is investigated, and the higher genus partition functions of an arbitrary permutation orbifold are expressed in terms of those of the original…