An effective Bertini theorem over finite fields.
An effective bound of p for algebraic points on Shimura curves of Γ₀(p)-type
In previous articles, we showed that for number fields in a certain large class, there are at most elliptic points on a Shimura curve of Γ₀(p)-type for every sufficiently large prime number p. In this article, we obtain an effective bound for such p.
An effective Matsusaka big theorem
An effective result of André-Oort type II
We prove some new effective results of André-Oort type. In particular, we state certain uniform improvements of the main result in [L. Kühne, Ann. of Math. 176 (2012), 651-671]. We also show that the equation X + Y = 1 has no solution in singular moduli. As a by-product, we indicate a simple trick rendering André's proof of the André-Oort conjecture effective. A significantly new aspect is the usage of both the Siegel-Tatuzawa theorem and the weak effective lower bound on the class number of an...
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.