Related papers: An elliptic second main theorem
We prove a duality formula between two elliptic determinants. We present a proof which is a variant of the Izergin-Korepin method which is a method originally introduced to analyze and compute partition functions of integrable lattice…
Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields.
An technically interesting proof of a known theorem.
We present an algorithm for constructing the fixed point of a general non-isometric similarity of the plane.
We give a new analytical proof of the Morse index theorem for geodesics in Riemannian manifolds.
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
We prove two theorems concerning isogenies of elliptic curves over function fields. The first one describes the variation of the height of the $j$-invariant in an isogeny class. The second one is an "isogeny estimate", providing an explicit…
We give a simple proof of the well-known divisibility by 2 condition for rational points on elliptic curves with rational 2-torsion. As an application of the explicit division by $2^n$ formulas obtained in Sec.2, we construct versal…
We prove a uniformization theorem in complex algebraic geometry.
The aim of this paper is to give an alternative proof of Kac's theorem for weighted projective lines (\cite{W}) over the complex field. The geometric realization of complex Lie algebras arising from derived categories (\cite{XXZ}) is…
A proof is given of Rosenthal's \(\ell_1\) theorem.
We prove a conjecture by De Giorgi on the elliptic regularization of semilinear wave equations in the finite-time case.
We prove some constructive results that on first and maybe even on second glance seem impossible.
In this note we study the connection between the existence of a projective reconstruction and the existence of a fundamental matrix satisfying the epipolar constraints.
The purpose of the present paper is to explain the fake projective plane constructed by J.H. Keum from the point of view of arithmetic ball quotients. Beside the ball quotient associated with the fake projective plane, we also analize two…
In this paper, we present a general method for obtaining addition theorems of the Weierstrass elliptic function $\wp(z)$ in terms of given parameters. We obtain the classical addition theorem for the Weierstrass elliptic function as a…
We derive a priori second order estimates for fully nonlinear elliptic equations which depend on the gradients of solutions in critical ways on Hermitian manifolds. The global estimates we obtained apply to an equation arising from a…
Using techniques of projective geometry, we give elementary proofs of two theorems concerning Hagge configurations.
We show that every projective Oka manifold is elliptic in the sense of Gromov. This gives an affirmative answer to a long-standing open question.
A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…