An effective Shafarevich theorem for elliptic curves
An effective Version of Faltings' Product Theorem.
An effective version of Nor's theorem.
An elementary proof of the Hilbert-Mumford criterion.
An elliptic surface of Mordell-Weil rank over the rational numbers
Néron showed that an elliptic surface with rank , and with base , and geometric genus , may be obtained by blowing up points in the plane. In this paper, we obtain parameterizations of the coefficients of the Weierstrass equations of such elliptic surfaces, in terms of the points. Manin also describes bases of the Mordell-Weil groups of these elliptic surfaces, in terms of the points ; we observe that, relative to the Weierstrass form of the equation,(with , and a basis can be found...
An embedding theorem for smooth projective toric varieties.
An Equivariant Lefschetz Formula for Finite Reductive Groups.
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
An estimate of approximation constants for p-adic and real varities.
An Euler-Poincaré Characteristic for Improper Intersections.
An example concerning a question of Zariski
An example of an arithmetic Fuchsian group.
An example of an asymptotically Chow unstable manifold with constant scalar curvature
Donaldson proved that if a polarized manifold has constant scalar curvature Kähler metrics in and its automorphism group is discrete, is asymptotically Chow stable. In this paper, we shall show an example which implies that the above result does not hold in the case where is not discrete.
An example of two homeomorphic, nondiffeomorphic complete intersection surfaces.
An Example of Unirational Surfaces in Characteristic p.
An existence theorem for Prym special divisors.
An exotic smooth structure on .
An explicit algebraic family of genus-one curves violating the Hasse principle
We prove that for any , the curvein is a genus curve violating the Hasse principle. An explicit Weierstrass model for its jacobian is given. The Shafarevich-Tate group of each contains a subgroup isomorphic to .
An explicit factorisation of the zeta functions of Dwork hypersurfaces
An explicit formula for period determinant
We consider a generic complex polynomial in two variables and a basis in the first homology group of a nonsingular level curve. We take an arbitrary tuple of homogeneous polynomial 1-forms of appropriate degrees so that their integrals over the basic cycles form a square matrix (of multivalued analytic functions of the level value). We give an explicit formula for the determinant of this matrix.